48 citations · 97 across the 10 of their papers we have counts for
Showing 2013Show all
2 papers · 1 filter
math.DS2013★ 1 cited
Lyapunov functions, shadowing, and topological stability
Alexey A. Petrov, Sergei Yu. Pilyugin
We use Lyapunov type functions to give new conditions under which a homeomorphism of a compact metric space has the shadowing property. These conditions are applied to establish th…
math.DS2013
Shadowing near nonhyperbolic fixed points
Alexey A. Petrov, Sergei Yu. Pilyugin
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 diff…