14 citations · 36 across the 10 of their papers we have counts for
14 papers
On the accumulation of separatrices by invariant circles
Anatole Katok, Raphaël Krikorian
Let be a smooth symplectic diffeomorphism of admitting a (non-split) separatrix associated to a hyperbolic fixed point. We prove that if is a perturbation of…
Survey on entropy-type invariants of sub-exponential growth in dynamical systems
Adam Kanigowski, Anatole Katok, Daren Wei
Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of s…
Flexibility of Lyapunov exponents
Jairo Bochi, Anatole Katok, Federico Rodriguez Hertz
We outline the flexibility program in smooth dynamics, focusing on flexibility of Lyapunov exponents for volume-preserving diffeomorphisms. We prove flexibility results for Anosov…
Flexibility of entropies for surfaces of negative curvature
Alena Erchenko, Anatole Katok
We consider a smooth closed surface of fixed genus with a Riemannian metric of negative curvature with fixed total area. The second author has shown that the…
The Fried average entropy and slow entropy for actions of higher rank abelian groups
Anatole Katok, Svetlana Katok, Federico Rodriguez Hertz
We consider two numerical entropy--type invariants for actions of $\Zk$, invariant under a choice of generators and well-adapted for smooth actions whose individual elements have p…
Analytic uniquely ergodic volume preserving maps on odd spheres
Bassam Fayad, Anatole Katok
We construct examples of volume-preserving uniquely ergodic (and hence minimal) real-analytic diffeomorphisms on odd-dimemsional spheres