Pith. sign in

REVIEW

The structure of pointwise recurrent expansive homeomorphisms

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2201.00110 v1 pith:C6WE7YVU submitted 2022-01-01 math.DS

The structure of pointwise recurrent expansive homeomorphisms

classification math.DS
keywords pointwiserecurrentexpansivesubshiftsystemthencompactconjugate
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

Let $X$ be a compact metric space and let $f:X\rightarrow X$ be a homeomorphism on $X$. We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X, f)$ is topologically conjugate to a subshift of some symbolic system. Moreover, if $f$ is pointwise positively recurrent, then the subshift is semisimple; a counterexample is given to show the necessity of positive recurrence to ensure the semisimilicity.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.