DCDS-B
Variational shadowing
Sergei Yu. Pilyugin
Discrete & Continuous Dynamical Systems - B 2010, 14(2): 733-737 doi: 10.3934/dcdsb.2010.14.733
We introduce a variational shadowing property of diffeomorphisms and show that this property is equivalent to structural stability. Bibliography: 8 titles.
keywords: structural stability. shadowing Dynamical systems
DCDS
Shadowing near nonhyperbolic fixed points
Alexey A. Petrov Sergei Yu. Pilyugin
Discrete & Continuous Dynamical Systems - A 2014, 34(9): 3761-3772 doi: 10.3934/dcds.2014.34.3761
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.
keywords: Lyapunov function. shadowing Dynamical system fixed point

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