Problem 73

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If f is Anosov and gf, does h(g)h(f)?

Comments

What is the definition of g~f ?

g~f means isotopic or homotopic?

True for f transitive Anosov and g smooth. Indeed, passing to a cover, one can assume that the bundles of f are orientable and therefore the entropy of f equals the log of the spectral radius homology (Ruelle-Sullivan), since g is smooth if follows that h(g)h(f) (Yomdim).  

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