Some Remarks on Anosov Families
Jeovanny de Jesus Muentes Acevedo, Raquel Ribeiro

TL;DR
This paper investigates specific classes of Anosov families, demonstrating their canonical coordinates, expansiveness, shadowing property, and existence of Markov partitions, thus advancing understanding of their dynamical structure.
Contribution
It proves that a particular class of Anosov families admits canonical coordinates, are expansive, satisfy shadowing, and have Markov partitions, providing new insights into their structure.
Findings
Existence of canonical coordinates for certain Anosov families
Anosov families are expansive
They satisfy the shadowing property and have Markov partitions
Abstract
We study Anosov families which are sequences of diffeomorphisms along compact Riemannian manifolds such that the tangent bundle split into expanding and contracting subspaces. In this paper we prove that a certain class of Anosov families: (i) admit canonical coordinates (ii) are expansive, (iii) satisfy the shadowing property, and (iv) exhibit a Markov partition.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals
