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Shadowing in the case of nontransverse intersection

Author: A. Petrov
Translated by: S. Yu. Pilyugin
Original publication: Algebra i Analiz, tom 27 (2015), nomer 1.
Journal: St. Petersburg Math. J. 27 (2016), 103-123
MSC (2010): Primary 37C50
Published electronically: December 7, 2015
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Abstract: An example of a diffeomorphism of a three-dimensional manifold is constructed with the following properties: (i) this diffeomorphism satisfies Axiom A; (ii) there exist two hyperbolic fixed points $ p_1$ and $ p_2$ such that the unstable manifold $ W^u(p_1)$ of $ p_1$ and the stable manifold $ W^s(p_2)$ of $ p_2$ are one-dimensional and have nonempty intersection, $ W^u(p_1)\cap W^s(p_2)\neq \varnothing $; and (iii) the diffeomorphism has the Hölder shadowing property with Hölder shadowing exponent $ 1/4$.

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Additional Information

A. Petrov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, 28 Universitetskiĭ pr., Petrodvoretz, 198504, St. Petersburg, Russia

Keywords: Dynamical systems, shadowing, nontransverse intersection, axiom A
Received by editor(s): March 4, 2014
Published electronically: December 7, 2015
Additional Notes: This research was supported by RFBR (project 12-01-00257) and by St. Petersburg State University (project
Article copyright: © Copyright 2015 American Mathematical Society