David Parmenter

University of Warwick

Gibbs measures for hyperbolic attractors defined by densities

Ergodic Theory and Dynamical Systems Seminar

13th October 2022, 2:00 pm – 3:00 pm
Fry Building, G07

In this talk I will describe a new construction of Gibbs measures for hyperbolic attractors generalizing the original construction due to Sinai, Ruelle and Bowen of SRB measures. The classical construction of the SRB measure is based on pushing forward the normalized volume on a piece of unstable manifold. By modifying the density at each step appropriately we show that the resulting measure is a prescribed Gibbs measure. To prove this we require a property on the growth rate of unstable manifolds.

This is joint work with Mark Pollicott.

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