On the Plaque Expansivity Conjecture

On the Plaque Expansivity Conjecture

It is one of the main properties of uniformly hyperbolic dynamics that points of two distinct trajectories cannot be uniformly close one to another. This characteristics of hyperbolic dynamics is called expansivity. Hirsch, Pugh and Shub, 1977, formulated the so-called Plaque Expansivity Conjecture,...

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Veröffentlicht in:arXiv.org 2024-12
1. Verfasser: Kryzhevich, Sergey
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Expansion
Isomorphism
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description It is one of the main properties of uniformly hyperbolic dynamics that points of two distinct trajectories cannot be uniformly close one to another. This characteristics of hyperbolic dynamics is called expansivity. Hirsch, Pugh and Shub, 1977, formulated the so-called Plaque Expansivity Conjecture, assuming that two invariant sequences of leaves of central manifolds, corresponding to a partially hyperbolic diffeomorphism, cannot be locally close. There are many important statements in the theory of partial hyperbolicity that can be proved provided Plaque Expansivity Conjecture holds true. Here we are proving this conjecture in its general form.
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subjects Expansion
Isomorphism
title On the Plaque Expansivity Conjecture
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