Symbolic extension of ${\mathcal{C}}^{1,\alpha }$ maps in arbitrary dimensions

Abstract

We prove that every ${\mathcal{C}}^{1,\alpha }$ self-map of a compact Riemannian manifold, in arbitrary dimension, admits a symbolic extension. This gives a positive answer to the conjecture of T. Downarowicz and S. Newhouse in arbitrary dimensions.

22pages, any comments or suggestions would be highly appreciated