Lipschitz shadowing implies structural stability

Abstract

We show that the Lipschitz shadowing property of a diffeomorphism is equivalent to structural stability. As a corollary, we show that an expansive diffeomorphism having the Lipschitz shadowing property is Anosov.

11 pages

References in corpus (1)

• Periodic shadowing and $\Omega$-stability

Cited by in corpus (9)

• Expansivity and Shadowing in Linear Dynamics
• Shadowing for infinite dimensional dynamics and exponential trichotomies
• On specification and measure expansiveness
• Holder Shadowing on Finite Intervals
• Shades of Hyperbolicity for Hamiltonians
• Conditional Lipschitz shadowing for ordinary differential equations
• Quasi-shadowing for partially hyperbolic dynamics on Banach spaces
• Some Consequences of the Shadowing Property in Low Dimensions
• Phase and frequency linear response theory for hyperbolic chaotic oscillators