A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class
ERGODIC THEORY AND DYNAMICAL SYSTEMS(2023)
Abstract
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/heteroclinic intersections from a chain recurrence class of a periodic point. The technique is first stated under a simpler setting called a Markov iterated function system, a two-dimensional iterated function system in which the compositions are chosen in a Markovian way. Then we apply the result to the setting of three-dimensional partially hyperbolic diffeomorphisms.
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Key words
hyperbolic chain recurrence class,horseshoe,mechanism
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