Optimal transport and dynamics of expanding circle maps acting on measures

Details Optimal transport and dynamics of expanding circle maps acting on measures Optimal transport and dynamics of expanding circle maps acting on measures

2010-06-23

arxiv.org/abs/1006.4491v3

Mathematics

Dynamical Systems

26 pages; v2 mainly corrects some typos; v3 many inaccuracies corrected, Theorem 1.4 added, second part cut into a separate pa

Scientific paper

Using optimal transport we study some dynamical properties of expanding circle maps acting on measures by push-forward. Using the definition of the tangent space to the space of measures introduced by Gigli, their derivative at the unique absolutely continuous invariant measure is computed. In particular it is shown that 1 is an eigenvalue of infinite multiplicity, so that the invariant measure admits many deformations into nearly invariant ones. We also prove that this action has positive metric mean dimension with respect to the Wasserstein metric.

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