July 2000

The accumulation of boundary doubling for modified tent maps

Paul Glendinning Department of Mathematics U.M.I.S.T. P.O. Box 88 Manchester M60 1QD, U.K.

Abstract

We describe the transition to chaos via boundary doubling for a particularly simple class of map. In this two parameter family of maps the accumulation of boundary doubling occurs on a curve in parameter space. We characterise this curve and relate the form of the curve to a novel set of difference equations with proportional delay.

    Email: p.a.glendinning@umist.ac.uk

Submitted to the Proceedings of the Conference on Bifurcations, Symmetry and Patterns, Porto, July 2000, in honour of M. Golubitsky and I. Stewart.