Alexey A. Petrov, Sergei Yu. Pilyugin
Published 2013-10-01, updated 2013-11-15Version 2
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.
Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points
Fractal analysis of hyperbolic and nonhyperbolic fixed points and singularities of dynamical systems in $\mathbb{R}^{n}$
Lyapunov functions, shadowing, and topological stability
![QR code for arXiv:1310.0496 [math.DS]](http://oss.arxitics.com/images/favicon.svg)