6533b828fe1ef96bd1288fdc

RESEARCH PRODUCT

A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class

Christian BonattiKatsutoshi Shinohara

subject

37B25 37D30 37G35FOS: Mathematics[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)Mathematics - Dynamical Systems

description

We give a $C^1$-perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/hetero-clinic intersections from a chain recurrence class of a periodic point. The technique is first stated under a simpler setting called Markov iterated function system, a two dimensional iterated function system in which the compositions are chosen in Markovian way. Then we apply the result to the setting of three dimensional partially hyperbolic diffeomorphisms.

yearjournalcountryeditionlanguage
2022-09-27
https://dx.doi.org/10.48550/arxiv.2209.13245