Shadowing near nonhyperbolic fixed points

Alexey A. Petrov; Sergei Yu. Pilyugin

doi:10.3934/dcds.2014.34.3761

Article Contents

2014, Volume 34, Issue 9: 3761-3772. Doi: 10.3934/dcds.2014.34.3761

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Shadowing near nonhyperbolic fixed points

Alexey A. Petrov^1, and
Sergei Yu. Pilyugin^2,

1.
Faculty of Mathematics and Mechanics St. Petersburg State University, University av., 28, 198504, St. Petersburg
2.
Faculty of Mathematics and Mechanics, St. Petersburg State University, University av. 28, 198504, St. Petersburg

Received: January 31, 2013

Revised: November 30, 2013

Published: August 2014

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Abstract

We use Lyapunov type functions to find conditions of finite shadowing in a neighborhood of a nonhyperbolic fixed point of a one-dimensional or two-dimensional homeomorphism or diffeomorphism. A new concept of shadowing in which we control the size of one-step errors is introduced in the case of a nonisolated fixed point.

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Mathematics Subject Classification: Primary: 37C50.

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References

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