Non-rigidity of partially hyperbolic abelian $C^1$-actions on tori

Abstract We prove that every genuinely partially hyperbolic $\mathbb {Z}^r$ -action by toral automorphisms can be perturbed in $C^1$ -topology, so that the resulting action is continuously conjugate, but not $C^1$ -conjugate, to the original one.

Authors

Publication Details

Journal
Ergodic Theory and Dynamical Systems
Published
2024-09-09
DOI
https://doi.org/10.1017/etds.2024.18
Primary Topic
Mathematical Dynamics and Fractals
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Non-rigidity of partially hyperbolic abelian $C^1$-actions on tori

Federico Rodriguez Hertz, Zhiren Wang
Ergodic Theory and Dynamical Systems
Mathematical Dynamics and Fractals
article

Non-rigidity of partially hyperbolic abelian $C^1$-actions on tori

Federico Rodriguez Hertz, Zhiren Wang
article en

Abstract

Abstract We prove that every genuinely partially hyperbolic $\mathbb {Z}^r$ -action by toral automorphisms can be perturbed in $C^1$ -topology, so that the resulting action is continuously conjugate, but not $C^1$ -conjugate, to the original one.

Ergodic Theory and Dynamical SystemsVol. 45(2)
Openalex Percentile: Top 74%
Mathematical Dynamics and Fractals
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Non-rigidity of partially hyperbolic abelian $C^1$-actions on tori — Federico Rodriguez Hertz, Zhiren Wang · Ergodic Theory and Dynamical Systems (2024) | TGRS Research Map | TGRS