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A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce $C^{r}$ open sets ( $r = 1, 2, \dots, \infty$ ) of symplectic diffeomorphisms and Hamiltonian systems, exhibitinglargerobustly transitive sets. We show that the $C^{\infty}$ closure of such open sets contains a variety of systems, including so-calleda priori unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of...

R-torsion and zeta functions for locally symmetric manifolds.

Henri Moscovici, Robert J. Stanton (1991)

Inventiones mathematicae

Saddle-focus singular cycles and prevalence of hyperbolicity

Bernardo San Martín (1998)

Annales de l'I.H.P. Analyse non linéaire

Saddles for expansive flows with the pseudo orbits tracing property

Jerzy Ombach (1991)

Annales Polonici Mathematici

Let F be an expansive flow with the pseudo orbits tracing property on a compact metric space X. Suppose X is connected, locally connected and contains at least two distinct orbits. Then any point is a saddle.

Scaling properties of a hybrid Fermi-Ulam-bouncer model.

Oliveira, Diego F.M., Bizão, Rafael A., Leonel, Edson D. (2009)

Mathematical Problems in Engineering

Scattering matrix for asymptotically euclidean manifolds

Richard Melrose, Maciej Zworski (1994)

Journées équations aux dérivées partielles

Second order linear differential systems

F. Neuman (1980)

Annales scientifiques de l'École Normale Supérieure

Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula

Frédéric Faure (2007)

Annales de l’institut Fourier

We consider a nonlinear area preserving Anosov map $M$ on the torus phase space, which is the simplest example of a fully chaotic dynamics. We are interested in the quantum dynamics for long time, generated by the unitary quantum propagator $\hat{M}$ . The usual semi-classical Trace formula expresses $T r ({\hat{M}}^{t})$ for finite time $t$ , in the limit $ℏ \to 0$ , in terms of periodic orbits of $M$ of period $t$ . Recent work reach time $t ≪ t_{E} / 6$ where $t_{E} = log (1 / ℏ) / λ$ is the Ehrenfest time, and $λ$ is the Lyapounov coefficient. Using a semi-classical normal form...

Semiconjugacy to a map of a constant slope

Jozef Bobok (2012)

Studia Mathematica

It is well known that any continuous piecewise monotone interval map f with positive topological entropy $h_{t o p} (f)$ is semiconjugate to some piecewise affine map with constant slope $e^{h_{t o p} (f)}$ . We prove this result for a class of Markov countably piecewise monotone continuous interval maps.

Shadowing lemma for family of $ε$ -trajectories

Tadek Nadzieja (1991)

Archivum Mathematicum

Shift spaces and attractors in noninvertible horseshoes

H. Bothe (1997)

Fundamenta Mathematicae

As is well known, a horseshoe map, i.e. a special injective reimbedding of the unit square $I^{2}$ in $ℝ^{2}$ (or more generally, of the cube $I^{m}$ in $ℝ^{m}$ ) as considered first by S. Smale [5], defines a shift dynamics on the maximal invariant subset of $I^{2}$ (or $I^{m}$ ). It is shown that this remains true almost surely for noninjective maps provided the contraction rate of the mapping in the stable direction is sufficiently strong, and bounds for this rate are given.

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Reversible Anosov diffeomorphisms and large deviations.

Rigid reparametrizations and cohomology for horocycle flows.

Rigidité différentiable des groupes fuchsiens

Rigidité du flot géodésique de certaines nilvariétés de rang deux

Robust controller design for modified projective synchronization of Chen-Lee chaotic systems with nonlinear inputs.

Robust transitivity in hamiltonian dynamics