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pith:UCL4CFON

pith:2026:UCL4CFONWP53FQFMZZ2VZLNRT7

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Metric mean dimension of factor maps

Rui Yang

Factor maps with infinite weighted topological entropy are characterized using three types of weighted metric mean dimensions that relate to those of the factor and extension systems.

arxiv:2605.17473 v1 · 2026-05-17 · math.DS

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Claims

C1strongest claim

We introduce three types of weighted metric mean dimensions to characterize factor maps with infinite weighted topological entropy, and compare them with the metric mean dimensions of the factor system and the extension system. Furthermore, we establish variational principles for weighted metric mean dimension. We introduce relative conditional metric mean dimension for factor maps with infinite relative topological conditional entropy, and prove that it coincides with relative metric mean dimension. In the context of random dynamical systems, we introduce random average metric mean dimension and use it to establish a topological Abramov-Rokhlin formula.

C2weakest assumption

The underlying dynamical systems possess infinite weighted topological entropy or infinite relative topological conditional entropy, allowing the new weighted and relative dimensions to be meaningfully defined and compared without reducing to standard finite-entropy cases.

C3one line summary

Introduces weighted metric mean dimensions and relative conditional metric mean dimension for factor maps with infinite entropy, proves variational principles and a topological Abramov-Rokhlin formula for random systems.

References

38 extracted · 38 resolved · 1 Pith anchors

[1] R. Adler, A. Konheim and M. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319 1965

[2] Arnold, Random dynamical systems, Springer, 1998 1998

[3] J. Barral and D. Feng, Weighted thermodynamic formalism on subshifts and applications, Asian J. Math. 16 (2012), 319-352 2012

[4] Bedford, Crinkly curves, Markov partitions and box dimension in self-similar sets, PhD Thesis, University of Warwick, 1984 1984

[5] Bogensch\" u tz and H 1992

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Receipt and verification

First computed	2026-05-20T00:04:40.832806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a097c115cdb3fbb2c0acce755cadb19fe3eaa19ace2f56441e532921857f1c85

Aliases

arxiv: 2605.17473 · arxiv_version: 2605.17473v1 · doi: 10.48550/arxiv.2605.17473 · pith_short_12: UCL4CFONWP53 · pith_short_16: UCL4CFONWP53FQFM · pith_short_8: UCL4CFON

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UCL4CFONWP53FQFMZZ2VZLNRT7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a097c115cdb3fbb2c0acce755cadb19fe3eaa19ace2f56441e532921857f1c85

Canonical record JSON

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    "abstract_canon_sha256": "b5e229aa64f41fbe3dfd1232feb4c47173601fdda813410a1e7e95de2b067990",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-17T14:21:36Z",
    "title_canon_sha256": "15599714d6e2af8df6fc291589e7e488f49da4da652de0b3947da7999af507e6"
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    "kind": "arxiv",
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