1 citations · 2 across the 11 of their papers we have counts for
12 papers
On the density of Lyapunov unstable elliptic equilibria
Bassam Fayad, Jaime Paradela, Maria Saprykina +1
We prove that any real-analytic Hamiltonian in five or more degrees-of-freedom, with a locally integrable non-degenerate elliptic equilibrium with indefinite quadratic part, can be…
KAM-rigidity for parabolic affine abelian actions
Danijela Damjanovic, Bassam Fayad, Maria Saprykina
We show the following dichotomy for a linear parabolic -action on the torus with at least one step-2 generator: (i) Any affine -action with linear p…
Nonconmutative coboundary equations over integrable systems
Rafael de la Llave, Maria Saprykina
\def\G{\mathcal G} \def\M{\mathcal M} \def\cE{\mathcal E} We prove an analog of Livšic theorem for real-analytic families of cocycles over an integrable system with values in a Ban…
Topological weak mixing and diffusion at all times for a class of Hamiltonian systems
Bassam Fayad, Maria Saprykina
We present examples of nearly integrable analytic Hamiltonian systems with several strong diffusion properties: topological weak mixing and diffusion at all times. These examples a…
Realizing arbitrary -dimensional dynamics by renormalization of -perturbations of identity
Bassam Fayad, Maria Saprykina
Any conservative map of the -dimensional unit ball can be realized by renormalized iteration of a perturbation of identity: there exists a conserva…
Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation
Rafael de la Llave, Maria Saprykina
Consider an analytic Hamiltonian system near its analytic invariant torus carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at $\ma…