Smooth rigidity for very non-algebraic expanding maps

TL;DR

This paper demonstrates that in the space of expanding maps, smooth conjugacy classes are generically characterized by Jacobians at periodic points, revealing a form of rigidity in non-algebraic settings.

Contribution

It establishes a smooth rigidity result for a broad class of non-algebraic expanding maps, linking conjugacy classes to Jacobian data at periodic points.

Findings

Open and dense set of maps with rigidity property

Conjugacy classes determined by Jacobians at periodic points

Applicable to very non-algebraic expanding maps

Abstract

We show that the space of expanding maps contains an open and dense set where smooth conjugacy classes of expanding maps are determined by the values of the Jacobians of return maps at periodic points.