Ergodic Theory and Dynamical Systems

Research Article

Unfoldings of discrete dynamical systems

Joel W. Robbina1

a1 Mathematics Department, University of Wisconsin, Madison, WI 53706, USA

Abstract

A universal unfolding of a discrete dynamical system f0 is a manifold F of dynamical systems such that each system g sufficiently near f0 is topologically conjugate to an element f of F with the conjugacy φ and the element f depending continuously on f0. An infinitesimally universal unfolding of f0 is (roughly speaking) a manifold F transversal to the topological conjugacy class of f0. Using Nash-Moser iteration we show infinitesimally universal unfoldings are universal and (in part II) give a class of examples relating to moduli of stability introduced by Palis and De Melo.

(Received September 15 1983)

(Revised March 01 1984)