T. Samuel (Bremen)

will speak on

Embedding the dynamics of Lorenz maps in linear systems

Time: 3:00PM
Date: Tue 12th February 2013
Location: [map]

Abstract: In 1965 Parry proved that any topological mixing interval map with a finite number of discontinuities is topologically conjugate to a unique piecewise continuous map $U: [0, 1] o [0,1]$ whose derivative is constant everywhere, apart from at a finite number of points. When restricting to Lorenz maps, Hubbard and Sparrow and independently Barnsley, Harding and Vince proved that the kneading sequence of the critical point fully determines $U$. In this talk I will begin by reviewing these results and then I would like to present recent joint work with Nina Snigireva and Andrew Vince. Necessary and sufficient conditions for the dynamics of a given Lorenz map to be fully embedded in the dynamics of a uniform Lorenz map will be discussed. As an application of this embedding result, we describe a simple algorithm for calculating the topological entropy of a Lorenz map. If time permits, the talk will then end with some related open questions, which Snigireva and I are currently working towards solving. (This is joint work with N. Snigireva (University College Dublin) and A. Vince (University of Florida)

(This talk is part of the Analysis series.)

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