Pith. sign in

Paper Citation Record · LEDGER

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures

As of 16 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:1908.00998.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.00998 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T15:34:24.633505Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

31 of 31 outbound references displayed

  • verified exact0
  • verified fuzzy22
  • unresolved9
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 313d5cd0-61f7-4c11-a8c1-e3125879bb5f · outbound

This paper cites Pointwise dimensions for Poincar´ e recurrences associated with maps and special flow s.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Pointwise dimensions for Poincar´ e recurrences associated with maps and special flow s

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.983565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.526506Z digest=sha256:03c7a1857383359341ee45be8a6439e05628704479c3c50f254b56b63b636e6f

Observation 6723df83-a207-421c-a6f0-4950099f2c64 · outbound

This paper cites Generalized fractal dimensions: equivalences and basic properties.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Generalized fractal dimensions: equivalences and basic properties

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.975108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.531259Z digest=sha256:8dc42c743a1de0d07107300fa81c0e700cd0caec07191d2d8d53f89b4f9c1c0f

Observation 48621542-9955-40d8-acd9-bfd0cb060a3b · outbound

This paper cites non-typical.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures non-typical

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.965567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.535027Z digest=sha256:4f7035835ea522a4a5f265f7bea060124f89f58b2324219de1c4beeb20f961fc

Observation 31ece8fe-ec9f-4260-803e-e661f2223206 · outbound

This paper cites Entropy for group endomorphisms and homoge neous spaces.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Entropy for group endomorphisms and homoge neous spaces

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.956361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.538809Z digest=sha256:3e7c924ca6e94df62262ea85368fc5cf9e9f491356dfbf10fc2d55931dcc2a38

Observation 943ddef8-2cf6-4acf-99c5-52102c690eb1 · outbound

This paper cites an unresolved cited work.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:34:24.944999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.542611Z digest=sha256:e390964f43f0a4899fc54c72fd729a9989398cf385ecc3b028623c5f3bc48b41

Observation d1feac3b-1198-4945-b2e4-941e67afa4a7 · outbound

This paper cites an unresolved cited work.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:34:24.933861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.546561Z digest=sha256:f6041016100080e1f2584685e227381e386d3078671524621ba8ee85ff547988

Observation a6c1e686-e21a-4e90-9d33-1e805a74d0ac · outbound

This paper cites an unresolved cited work.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:34:24.923722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.550717Z digest=sha256:9e9d51e4dfd781635354d6eb9071c263bf0a3af3556d13e134d3c591c6980cd2

Observation 22f8bb5c-54c9-4c0c-85be-4f9dd5e63af0 · outbound

This paper cites Ergodic theory on compact spaces.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Ergodic theory on compact spaces

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.913666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.555102Z digest=sha256:ace542c1ee9cdeb0a46f5b0154e4458dc1297fa7eab4730fbeb629f765a64c1c

Observation 6430689a-90fd-45c7-be8e-0dba46da5267 · outbound

This paper cites Some compact invariant sets for hyperboli c linear automorphisms of torii [tori].

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Some compact invariant sets for hyperboli c linear automorphisms of torii [tori]

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.902996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.558773Z digest=sha256:8d97b88828a3818afa7330571a0004e251681d894be94659a76ed5e5c27d0510

Observation 507bfcab-9ae8-4560-9367-f491115e594a · outbound

This paper cites Expansiveness, hyperbolicity and Hausd orff dimension.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Expansiveness, hyperbolicity and Hausd orff dimension

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.891476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.562549Z digest=sha256:369b1d53c16011f0f0f30aa5e9ac58f2bb6f6d4d6c1e102083ab75732963a584

Observation 712e3426-2687-4161-9286-cd4ab5832955 · outbound

This paper cites Lyapunov functions and topological st ability.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Lyapunov functions and topological st ability

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.874035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.566269Z digest=sha256:670cda3887186a821479b0110bdb181d21c1e5aceaa9112fb91c3a397a613517

Observation 20c4b16e-b6f9-449f-99c8-d65f1632f309 · outbound

This paper cites D imension of a measure.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures D imension of a measure

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.861850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.569700Z digest=sha256:37ad8b8250da6288b8dfd6c15ee8e23f5860cc9a3a966fb6f023e40241a71263

Observation 56ed4a0e-3181-4bdc-b872-6c28a2bf1e4d · outbound

This paper cites An introduction to and comparison of three not ions of dimension in metric spaces.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures An introduction to and comparison of three not ions of dimension in metric spaces

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.850362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.572540Z digest=sha256:2c5448718e83d30ef41ad16637b176759c263f38285c14d3ded357ef6d0f675f

Observation 75aeed68-09f6-4147-af12-d9f0c636b835 · outbound

This paper cites an unresolved cited work.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:34:24.840332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.575710Z digest=sha256:35a51c4952f5a55a7bcb920c003b8ddea639f619ee9f70d97b541befa7544fbb

Observation 18451104-d4e6-4e6b-98fa-4aa275df649d · outbound

This paper cites Pesin and A.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Pesin and A

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.830820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.578883Z digest=sha256:6fea8399d3767bf2d882986cd4eeef399835fb3bd2b51a7202d438614a86844f

Observation 0628aacc-356b-4731-940d-a29c8dab6757 · outbound

This paper cites an unresolved cited work.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:34:24.820951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.582025Z digest=sha256:818e946e2f3e1c02d6f2fc95cdc80de62fcd2ad002c517e65f7e12eb33a9e152

Observation ac684ac0-493e-4b02-ba10-38dccd233001 · outbound

This paper cites an unresolved cited work.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:34:24.810714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.585043Z digest=sha256:44bf5981499053344b19963635222c00be5590ea07b9f4913a37e31e9e5fd942

Observation 63eaaeca-a212-4550-9e25-a07559e9d561 · outbound

This paper cites an unresolved cited work.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:34:24.800614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.588734Z digest=sha256:9902da25928d44f3da21924fad85e548e6f400dcf3f79952ba8bd8d2a139f7ca

Observation e9372f0b-c635-42c5-88aa-753ac96cd739 · outbound

This paper cites Ruelle’s inequality in negative curv ature.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Ruelle’s inequality in negative curv ature

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.790196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.591943Z digest=sha256:0b372e7c23ba5068cbaeb0c9d7772ca6c6acbf0f26b7eaae5f64254060a09838

Observation 8684a79a-afd6-47d6-a6d1-09ae726e742d · outbound

This paper cites Pointwise dimensions and R´ enyi dim ensions.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Pointwise dimensions and R´ enyi dim ensions

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.778548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.596191Z digest=sha256:01b627fbc7a84bc005ab59e17e1badea36c458a02edb209d61845ef0de7e9218

Observation cc9c2377-7a29-48a6-b9d7-08c25d621318 · outbound

This paper cites Recurrence rate in rapidly mixing dyn amical systems.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Recurrence rate in rapidly mixing dyn amical systems

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.766787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.599673Z digest=sha256:7a7de23a23042934905edeb26940e4ab9713781afcca1300fe59b26b0a48936f

Observation bce03c76-b7a0-41d5-a7d3-db90bf5c7784 · outbound

This paper cites Generic properties of invariant measure s for Axiom A diffeomorphisms.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Generic properties of invariant measure s for Axiom A diffeomorphisms

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.756070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.603366Z digest=sha256:4eaf5dcfef91d0f5876b38f9909a496005bbd88a6d623485337fcd890a80690a

Observation 602c3876-c84f-4c8a-a25b-d13185a3e69c · outbound

This paper cites On the prevalence of zero entropy.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures On the prevalence of zero entropy

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.745859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.606771Z digest=sha256:0a5ed02a54564f6863f98741ad3fdb50a2afce29650cee46a35b492b2a8b5dcb

Observation 034cbb2c-5c89-4a4f-8893-9d95f652dd41 · outbound

This paper cites On mixing measures for axiom A diffeomorphi sms.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures On mixing measures for axiom A diffeomorphi sms

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.734512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.610280Z digest=sha256:c6fc01e8dea3be0b49807a62bbb8a7d469c4ab5b0277e24c0097549d46457a48

Observation f0037849-bdb0-4af0-9722-a1cde628d70f · outbound

This paper cites On dynamical systems with the specificati on property.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures On dynamical systems with the specificati on property

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.723683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.613819Z digest=sha256:41fe5956574111c971842070fdc9dc36ea50dd74c23a4e9da2d865cea8d3b3fb

Observation 4fc50d5e-25f7-419d-bc11-5b98de17ea89 · outbound

This paper cites Correlation dimension.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Correlation dimension

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.714451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.617105Z digest=sha256:b3d2ba90c004ae1d952d881392a20dd1e725d23a165af89273a944955dfcb417

Observation fe48f0a5-0a19-447f-89a6-8f4c8794c361 · outbound

This paper cites Multifractal anal ysis of local entropies for expansive homeomorphisms with specification.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Multifractal anal ysis of local entropies for expansive homeomorphisms with specification

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.704944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.620419Z digest=sha256:d1c915ba3d39a74884344b5300b046483edb173250082de0760a32c7c9d57732

Observation 76d76bf5-6e62-43c5-915e-f45f1b2a4bb5 · outbound

This paper cites Generalized entropies in dynamica l systems.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Generalized entropies in dynamica l systems

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.695369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.623695Z digest=sha256:f3149b19dcd2843bd104e9ea57e0af9bcbfa872d26cde0ad346c148f03325d5c

Observation 68b14c4c-cce5-4617-8da1-3c09be8432dd · outbound

This paper cites An introduction to ergodic theory , volume 79 of Graduate Texts in Mathe- matics.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures An introduction to ergodic theory , volume 79 of Graduate Texts in Mathe- matics

Reference 29

Resolution
unresolved
no resolver link, observed 2026-08-14T15:34:24.626833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T15:34:24.626833Z digest=sha256:8a2119ad0fd4dddb61f8928725f8adc5cb773bb69649db9feba4684758db0a0b

Observation f0e9140c-c40e-448d-ba94-886be1ba98a4 · outbound

This paper cites an unresolved cited work.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:34:24.676461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.630380Z digest=sha256:5d43b2c596795e693d94302f442024f3a5852688fd4ff433b92dc534e0e890a1

Observation 49cdbf55-a159-478b-ac2b-de6e42ff1e29 · outbound

This paper cites Dimension, entropy and Lyapunov expone nts.

A note on the relation between the metric entropy and the generalized fractal dimensions of invariant measures Dimension, entropy and Lyapunov expone nts

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:34:24.665362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T15:34:24.633505Z digest=sha256:26933b3b5d4161d827c1942b0a7e9225ec765202546c2dd839ea5ba7f51565a3

Pith citing papers

No inbound Pith citation observations are available.