45 citations · 194 across the 35 of their papers we have counts for
15 papers · 1 filter
Entropy collapse versus entropy rigidity for Reeb and Finsler flows
Alberto Abbondandolo, Marcelo R. R. Alves, Murat Saglam +1
On every closed contact manifold there exist contact forms with volume one whose Reeb flows have arbitrarily small topological entropy. In contrast, for many closed manifolds there…
Stable foliations and CW-structure induced by a Morse-Smale gradient-like flow
Alberto Abbondandolo, Pietro Majer
We prove that a Morse-Smale gradient-like flow on a closed manifold has a "system of compatible invariant stable foliations" that is analogous to the object introduced by Palis and…
The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere
Alberto Abbondandolo, Luca Asselle, Gabriele Benedetti +2
We consider magnetic Tonelli Hamiltonian systems on the cotangent bundle of the 2-sphere, where the magnetic form is not necessarily exact. It is known that, on very low and on hig…
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…
Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level
Alberto Abbondandolo, Leonardo Macarini, Marco Mazzucchelli +1
We consider an exact magnetic flow on the tangent bundle of a closed surface. We prove that for almost every energy level below the Mañé critical value of the universal cover t…
Lectures on the free period Lagrangian action functional
Alberto Abbondandolo
In this expository article we study the question of the existence of periodic orbits of prescribed energy for classical Hamiltonian systems on compact configuration spaces. We use…