A limit set trichotomy for order-preserving systems on time scales.
A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs
For large N, we consider the ordinary continued fraction of x=p/q with 1≤p≤q≤N, or, equivalently, Euclid’s gcd algorithm for two integers 1≤p≤q≤N, putting the uniform distribution on the set of p and qs. We study the distribution of the total cost of execution of the algorithm for an additive cost function c on the set ℤ+* of possible digits, asymptotically for N→∞. If c is nonlattice and satisfies mild growth conditions, the local limit theorem was proved previously by the second named author....
A locally commutative free group acting on the plane
The purpose of this paper is to prove the existence of a free subgroup of the group of all affine transformations on the plane with determinant 1 such that the action of the subgroup is locally commutative.
A natural occurrence of shift equivalence
A natural occcurrence of shift equivalence in a purely algebraic setting is exhibited.
A new approach to the Ricci flow on
A new proof of the Aubry-Mather's theorem.
A non-linear discrete-time dynamical system related to epidemic SISI model
We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.
A note on dynamical zeta functions for S-unimodal maps
Let f be a nonrenormalizable S-unimodal map. We prove that f is a Collet-Eckmann map if its dynamical zeta function looks like that of a uniformly hyperbolic map.
A note on LaSalle's problems
In LaSalle's book "The Stability of Dynamical Systems", the author gives four conditions which imply that the origin of a discrete dynamical system defined on ℝ is a global attractor, and proposes to study the natural extensions of these conditions in ℝⁿ. Although some partial results are obtained in previous papers, as far as we know, the problem is not completely settled. In this work we first study the four conditions and prove that just one of them implies that the origin is a global attractor...
A note on pseudo-Anosov maps with small growth rate.
A note on stable iterated function systems.
A note on the construction of nonsingular Gibbs measures
We give a sufficient condition for the construction of Markov fibred systems using countable Markov partitions with locally bounded distortion.
A note on the fundamental matrix of variational equations in
The paper is devoted to the question whether some kind of additional information makes it possible to determine the fundamental matrix of variational equations in . An application concerning computation of a derivative of a scalar Poincaré mapping is given.
A note on the global attractivity of a discrete model of Nicholson's blowflies.
A note on the reducibility of linear differential equations with quasiperiodic coefficients.
A note on unimodal mappings with infinitely many attractors
A polynomial class of Markus-Yamabe counterexamples.
In the paper [CEGHM] a polynomial counterexample to the Markus-Yamabe Conjecture and to the discrete Markus-Yamabe Question in dimension n ≥ 3 are given. In the present paper we explain a way for obtaining a family of polynomial counterexamples containing the above ones. Finally we study the global dynamics of the examples given in [CEGHM].
A probabilistic and geometric perspective.
A projectively natural flow for circle diffeomorphisms.
A proof existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable hamiltonian systems.