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The sixth Painleve equation: a chaotic dynamical system

Tuesday 19th September 2006 - 16:30 to 17:30
INI Seminar Room 1

We show that the Poincare return map of the sixth Painleve equation is chaotic along almost every loop, called a non-elementary loop, in the domain of definition. For each such map we construct a natural invariant Borel probability measure and establish some dynamical properties of it such as positivity of the entropy, ergodicity, hyperbolicity, and so on. We also give an algorithm to calculate the entropy in terms of a reduced word of the loop. This is a joint work with my research student Takato Uehara.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons