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 occcurrence of shift equivalence in a purely algebraic setting is exhibited.
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.
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.
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...
We give a sufficient condition for the construction of Markov fibred systems using countable Markov partitions with locally bounded distortion.
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.
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].