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Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.

6 votes
2 answers
2k views

Relation between Hausdorff dimension and Bowen's equation

I am reading the paper Hausdorff dimension for Horseshoes, by McCluskey and Manning. In the following theorem Theorem: Let $\Lambda$ be a basic set for a $C^1$ axiom A diffeomorphism $f:M^2\to M^ …
4 votes
1 answer
286 views

Local product structure horseshoes

I am reading the paper: The Hausdorff dimension of horseshoes of Diffeomorphism of surfaces, Bulletin Brazilian Mathematical Society, Ricardo Mañe,(1990). Roughly speaking the author state that, the u …