In contrast to the time-dependent case, the time-t-section of Mañé set of autonomous
Lagrangian systems is independent of time, thus, it is nowhere disconnected. This causes …

We show the genericity from the viewpoint of Mañé of generic properties (as symplectic
linear maps) of the differential of Poincaré maps of periodic orbits of Hamiltonians …

We study Livsic's problem of finding, where is a given Anosov vector field. We show that, if
are analytic, then is analytic. We use the previous result to show that if two low-dimensional …

We prove that the Aubry and Mañé sets introduced by Mather in Lagrangian dynamics are
symplectic invariants. In order to do so, we introduce a barrier on phase space. This is also …

In this setting, he has obtained the existence of families of invariant sets generalizing the
well known Aubry-Mather invariant sets of twist maps. Then he stated in 1993 a result on the …

Invariants for smooth conjugacy of hyperbolic dynamical systems. IV Page 1 Commun. Math.
Phys. 116, 185-192 (1988) Communications in Mathematical Phys s © Springer-Verlag 1988 …

We construct the Green bundles for an energy level without conjugate points of a convex
Hamiltonian. In this case we give a formula for the metric entropy of the Liouville measure …

We consider Holder continuous GL (2, R)-valued cocycles over a transitive Anosov
diffeomorphism. We give a complete classification up to Holder cohomology of cocycles with …

Let L be a C∞ convex superlinear Lagrangian on a closed manifold M. We show that if the
number of static classes is finite, then there exist chains of semistatic orbits that connect any …

We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called
time-evolution operator K. This new approach unifies both the Lagrangian and the …