Diffusion to infinity for periodic orbits in meromorphic dynamics

• Autorzy: Janina Kotus , Grzegorz Świątek
• Języki publikacji: EN

Abstrakty

EN

A small perturbation of a rational function causes only a small perturbation of its periodic orbits. We show that the situation is different for transcendental maps. Namely, orbits may escape to infinity under small perturbations of parameters. We show examples where this "diffusion to infinity" occurs and prove certain conditions under which it does not.

Kategorie tematyczne

• 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
• 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
• 32H50: Iteration problems
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 174
• Numer: 3
• Strony: 263-269

Daty

wydano

2002

Twórcy

autor

Janina Kotus

• Department of Mathematics, Warsaw University of Technology, 00-661 Warszawa, Poland

autor

Grzegorz Świątek

• Department of Mathematics, Penn State University, University Park, PA 16802, U.S.A.

Identyfikatory

DOI

10.4064/fm174-3-6