6 citations · 15 across the 8 of their papers we have counts for
8 papers · 1 filter
Totally integrable symplectic billiards are ellipses
Luca Baracco, Olga Bernardi
In this paper we prove that a totally integrable strictly-convex symplectic billiard table, whose boundary has everywhere strictly positive curvature, must be an ellipse. The proof…
A Conley-type Lyapunov function for the strong chain recurrent set
Olga Bernardi, Anna Florio, Jim Wiseman
Let be a continuous flow on a compact metric space . In this article we constructively prove the existence of a continuous Lyapunov funct…
The generalized recurrent set, explosions and Lyapunov functions
Olga Bernardi, Anna Florio, Jim Wiseman
We consider explosions in the generalized recurrent set for homeomorphisms on a compact metric space. We provide multiple examples to show that such explosions can occur, in contra…
Existence of Lipschitz continuous Lyapunov functions strict outside the strong chain recurrent set
Olga Bernardi, Anna Florio
The aim of this paper is to study in detail the relations between strong chain recurrence for flows and Lyapunov functions. For a continuous flow on a compact metric space, uniform…
A Conley-type decomposition of the strong chain recurrent set
Olga Bernardi, Anna Florio
For a continuous flow on a compact metric space, the aim of this paper is to prove a Conley-type decomposition of the strong chain recurrent set. We first discuss in details the ma…
Chain recurrence, chain transitivity, Lyapunov functions and rigidity of Lagrangian submanifolds of optical hypersurfaces
Alberto Abbondandolo, Olga Bernardi, Franco Cardin
The aim of this paper is twofold. On the one hand, we discuss the notions of strong chain recurrence and strong chain transitivity for flows on metric spaces, together with their c…