Rigidity of isotropic maps

Rigidity of Infinitesimal Momentum Maps

In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, this yields rigidity also for lifted actions to the symplectic groupoid.

On Rigidity of One-Dimensional Maps

The regularity of the conjugacy between two onedimensional maps with singular points is considered. We prove that the conjugacy between two nice and mixing quasi-hyperbolic one-dimensional maps is a diffeomorphism if it is an absolutely continuous homeomorphism and the exponents and the asymmetries of these two maps at all corresponding singular points are the same. We also discuss the applicat...

Rigidity for Infinitely Renormalizable Area-preserving Maps

The period doubling Cantor sets of strongly dissipative Hénon-like maps with different average Jacobian are not smoothly conjugated. The Jacobian Rigidity Conjecture says that the period doubling Cantor sets of two-dimensional Hénon-like maps with the same average Jacobian are smoothly conjugated. This conjecture is true for average Jacobian zero, e.g. the onedimensional case. The other extreme...

Smooth Cocycle Rigidity for Expanding Maps, and an Application to Mostow Rigidity

We consider the Livsic cocycle equation, with values in compact Lie groups, and dynamics given by a piecewise-smooth expanding Markov map. We prove that any measurable solution to this equation must necessarily have a smooth version. We deduce a smooth rigidity theorem for conjugacies between piecewise-conformal expanding Markov maps, and apply this to give a variation on the proof of Mostow's ...

Piecewise monotone maps without periodic points: Rigidity, measures and complexity.