Partial hyperbolicity and homoclinic tangencies
We show that any diffeomorphism of a compact manifold can be approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.
Partial hyperbolicity for symplectic diffeomorphisms
Partition sensitivity for measurable maps
We study countable partitions for measurable maps on measure spaces such that, for every point , the set of points with the same itinerary as that of is negligible. We prove in nonatomic probability spaces that every strong generator (Parry, W., Aperiodic transformations and generators, J. London Math. Soc. 43 (1968), 191–194) satisfies this property (but not conversely). In addition, measurable maps carrying partitions with this property are aperiodic and their corresponding spaces are nonatomic....
Periodic billiard orbits in right triangles
There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards orbits are dense in the phase space, (ii) there is a unique nonsingular perpendicular billiard orbit which is not periodic, and (iii) the perpendicular periodic orbits fill the corresponding invariant surface.
Periodic orbits of renormalisation for the correlations of strange nonchaotic attractors.
Periodic points and chaotic-like dynamics of planar maps associated to nonlinear Hill's equations with indefinite weight.
Periods of Morse-Smale diffeomorphisms of 𝕊²
The aim of this paper is to describe the set of periods of a Morse-Smale diffeomorphism of the two-dimensional sphere according to its homotopy class. The main tool for proving this is the Lefschetz fixed point theory.
Periods of periodic points for transitive degree one maps of the circle with a fixed point.
Persistance des sous-variétés à bord et à coins normalement dilatées
On se propose de montrer que les variétés à bord et plus généralement à coins, normalement dilatées par un endomorphisme sont persistantes en tant que stratifications -régulières. Ce résultat sera démontré en classe , pour . On donne aussi un exemple simple d’une sous-variété à bord normalement dilatée mais qui n’est pas persistante en tant que sous-variété différentiable.
Persistence of invariant manifolds for perturbations of semiflows with symmetry.
Perturbations of flexible Lattès maps
We prove that any Lattès map can be approximated by strictly postcritically finite rational maps which are not Lattès maps.
Pesin theory and equilibrium measures on the interval
We use Pesin theory to study possible equilibrium measures for a broad class of piecewise monotone maps of the interval and a broad class of potentials.
Phase multistability of synchronous chaotic oscillations.
Phase synchronization in coupled Sprott chaotic systems presented by fractional differential equations.
Physical measures for infinite-modal maps
We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they satisfy the...
Planar Lorentz process in a random scenery
We consider the periodic planar Lorentz process with convex obstacles (and with finite horizon). In this model, a point particle moves freely with elastic reflection at the fixed convex obstacles. The random scenery is given by a sequence of independent, identically distributed, centered random variables with finite and non-null variance. To each obstacle, we associate one of these random variables. We suppose that each time the particle hits an obstacle, it wins the amount given by the random variable...
Plane affine geometry and Anosov flows
Plenty of elliptic islands for the standard family of area preserving maps
Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time
We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature...
Poincaré-Hopf index and partial hyperbolicity
We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index for vector fields with isolated zeroes in a -ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.