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A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 44 / Issue 8 / August 2024
- Published online by Cambridge University Press:
- 03 November 2023, pp. 2080-2142
- Print publication:
- August 2024
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- Article
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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.
