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Mathematics  2014 

Cohomology-free diffeomorphisms on tori

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Abstract:

A smooth diffeomorphism f of a smooth closed orientable manifold M is cohomology-free diffeomorphism (c.f) if for each smooth function g on M there exists a smooth function h on M and a constant c such that h-h o f = g. In this article we show that (c.f) diffeomorphisms on tori are conjugate to Diophantine translations. This is part of a conjecture of A. Katok [H, Problem 17]. We also show that a strictly ergodic diffeomorphism has topological entropy zero. This was question of M. Herman.

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