Rigorous numerical studies of the dynamics of polynomial skew products of C^2

Abstract

For the class of polynomial skew products of C^2, we describe a rigorous computer algorithm which, for a given map F, will (1) build a model of the dynamics of F on its chain recurrent set, and (2) attempt to determine whether F is Axiom A. Further, we discuss how we used our implementation of this algorithm to establish Axiom A for several explicit cases.

15 pages, 12 figures, submitted

References in corpus (1)

• Constructing an expanding metric for dynamical systems in one complex variable

Cited by in corpus (1)

• Axiom A polynomial skew products of C^2 and their postcritical sets