Affine diffeomorphisms of translation surfaces : periodic points, fuchsian groups, and arithmeticity
Algebraic periods of self-maps of a rational exterior space of rank 2.
Algebraic properties of the Lefschetz zeta function, periodic points and topological entropy.
The Lefschetz zeta function associated to a continuous self-map f of a compact manifold is a rational function P/Q. According to the parity of the degrees of the polynomials P and Q, we analyze when the set of periodic points of f is infinite and when the topological entropy is positive.
All solenoids of piecewise smooth maps are period doubling
We show that piecewise smooth maps with a finite number of pieces of monotonicity and nowhere vanishing Lipschitz continuous derivative can have only period doubling solenoids. The proof is based on the fact that if is a periodic orbit of a continuous map f then there is a union set of some periodic orbits of f such that for any i.
Almost localization and almost reducibility
Almost sure rates of mixing for i.i.d. unimodal maps
An analogue of the Variational Principle for group and pseudogroup actions
We generalize to the case of finitely generated groups of homeomorphisms the notion of a local measure entropy introduced by Brin and Katok [7] for a single map. We apply the theory of dimensional type characteristics of a dynamical system elaborated by Pesin [25] to obtain a relationship between the topological entropy of a pseudogroup and a group of homeomorphisms of a metric space, defined by Ghys, Langevin and Walczak in [12], and its local measure entropies. We prove an analogue of the Variational...
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings. (Summary).
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings.
An elementary proof of a Lima's theorem for surfaces.
An elementary proof of the following theorem is given:THEOREM. Let M be a compact connected surface without boundary. Consider a C∞ action of Rn on M. Then, if the Euler-Poincaré characteristic of M is non zero there exists a fixed point.
An example of a conservative exact endomorphism which is not lim sup full.
An extension of the Artin-Mazur theorem.
An isomorphism between polynomial eigenfunctions of the transfer operator and the Eichler cohomology for modular groups.
An -theory of the generalized Stokes resolvent system in infinite cylinders
Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with , a bounded domain of class , are obtained in the space , q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.
An ordered structure of rank two related to Dulac's Problem
For a vector field ξ on ℝ² we construct, under certain assumptions on ξ, an ordered model-theoretic structure associated to the flow of ξ. We do this in such a way that the set of all limit cycles of ξ is represented by a definable set. This allows us to give two restatements of Dulac’s Problem for ξ - that is, the question whether ξ has finitely many limit cycles-in model-theoretic terms, one involving the recently developed notion of -rank and the other involving the notion of o-minimality.
Analysis of an on-off intermittency system with adjustable state levels
We consider a chaotic system with a double-scroll attractor proposed by Elwakil, composing with a second-order system, which has low-dimensional multiple invariant subspaces and multi-level on-off intermittency. This type of composite system always includes a skew-product structure and some invariant subspaces, which are associated with different levels of laminar phase. In order for the level of laminar phase be adjustable, we adopt a nonlinear function with saturation characteristic to tune the...
Analytic invariants for the resonance
Associated to analytic Hamiltonian vector fields in having an equilibrium point satisfying a non semisimple resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.
Analytic torsions on contact manifolds
We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray–Singer torsion on any -dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact the whole spectral torsion function we consider may be interpreted on CR Seifert manifolds as a purely dynamical function through Selberg-like trace formulae, that hold also in variable...
Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms
We study spectral properties of transfer operators for diffeomorphisms on a Riemannian manifold . Suppose that is an isolated hyperbolic subset for , with a compact isolating neighborhood . We first introduce Banach spaces of distributions supported on , which are anisotropic versions of the usual space of functions and of the generalized Sobolev spaces , respectively. We then show that the transfer operators associated to and a smooth weight extend boundedly to these spaces, and...
Anosov endomorphisms