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arXiv · 1310.0496

Shadowing near nonhyperbolic fixed points

Alexey A. Petrov·Sergei Yu. Pilyugin
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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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Alexey A. Petrov, Sergei Yu. Pilyugin. 2013-11-15. Shadowing near nonhyperbolic fixed points. https://arxiv.org/abs/1310.0496

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