Source Themes

Generalized u-Gibbs measures for smooth diffeomorphisms

We show that for every $C^\infty$ diffeomorphism of a closed Riemannian manifold, if there exists a positive volume set of points which admit some expansion with a positive Lyapunov exponent (in a weak sense) then there exists an invariant …

SRB measures for partially hyperbolic diffeomorphisms with one dimensional center subbundles

SRB measures for mostly expanding partially hyperbolic diffeomorphisms via the variational approach

Habilitation Thesis

Multiplicity of topological systems

We define the topological multiplicity of an invertible topological system (X, T ) as the minimal number $k$ of real continuous functions $f_1, \cdots , f_k$ such that the functions $f_i\circ T^n$, $n \in \mathbb Z$, $1 \leq i \leq k$, span a dense …

Mean dimension of induced systems

For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak-$*$ topology has infinite topological mean dimension. We also estimate the rate of divergence …

Maximal measure and entropic continuity of Lyapunov exponents For $C^r$ surface diffeomorphisms with large entropy

We prove a finite smooth version of the entropic continuity of Lyapunov exponents of Buzzi-Crovisier-Sarig for $C^\infty$ surface diffeomorphisms [9]. As a consequence we show that any $C^r$, $r1$, smooth surface diffeomorphism $f$ with …

SRB measures for smooth surface diffeomorphisms

A $C^\infty$ surface diffeomorphism admits a SRB measure if and only if the set $\{x, \ \limsup_n\frac{1}{n}\log \|d_xf^n\|0 \}$ has positive Lebesgue measure. Moreover the basins of the ergodic SRB measures are covering this set Lebesgue almost …

Mean dimension of continuous automata

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Zero dimensional and symbolic extensions for topological flows