Families of One-Dimensional Maps and Nearby Diffeomorphisms
نویسنده
چکیده
1. Introduction. In the last decade, one-dimensional dynamical systems have been studied intensely from different points of view. One of the reasons for this interest is that the results about one-dimensional systems prove to be useful when studying multidimensional systems which act contractively in all but one direction. We shall call such systems near to one-dimensional. In this paper we present some results concerning one-dimensional maps and nearby diffeomorphisms. Consider some one-dimensional map f E C k (R, R), 1 < k < oo, and let a singular map / E C fc (R m , R m),
منابع مشابه
Chaotic attractors of relaxation oscillators
We develop a general technique for proving the existence of chaotic attractors for three-dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two-dimensional Henon-like maps are diffeomorphisms that limit on non-invert...
متن کاملm at h . D S ] 2 8 M ay 1 99 2 Polynomial Diffeomorphisms of C 2 . IV : The Measure of Maximal Entropy and Laminar Currents
The simplest holomorphic dynamical systems which display interesting behavior are the polynomial maps of C. The dynamical study of these maps began with Fatou and Julia in the 1920’s and is currently a very active area of research. If we are interested in studying invertible holomorphic dynamical systems, then the simplest examples with interesting behavior are probably the polynomial diffeomor...
متن کاملComputation of derivatives of the rotation number for parametric families of circle diffeomorphisms
In this paper we present a numerical method to compute derivatives of the rotation number for parametric families of circle diffeomorphisms with high accuracy. Our methodology is an extension of a recently developed approach to compute rotation numbers based on suitable averages of iterates of the map and Richardson extrapolation. We focus on analytic circle diffeomorphisms, but the method also...
متن کاملTorus Maps from Weak Coupling of Strong Resonances
This paper investigates a family of diffeomorphisms of the two dimensional torus derived from a model of an array of driven, coupled lasers (Braiman et al. 1995). It gives a negative answer to a question raised by Baesens et al. (1991a) about two parameter families of diffeomorphisms and flows of the two dimensional torus by exhibiting resonance regions in which the two parameter family has no ...
متن کاملExtremal Lyapunov Exponents: an Invariance Principle and Applications
We propose a new approach to analyzing dynamical systems that combine hyperbolic and non-hyperbolic (“center”) behavior, e.g. partially hyperbolic diffeomorphisms. A number of applications illustrate its power. We find that any ergodic automorphism of the 4-torus with two eigenvalues in the unit circle is stably Bernoulli among symplectic maps. Indeed, any nearby symplectic map has no zero Lyap...
متن کامل