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math.DS2026
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…
math.DS2026
Kolmogorov invariant torus theorem for weakly interacting particles I: Full dimensional tori
Dmitry Dolgopyat, Bassam Fayad, Jaime Paradela
We develop an abstract KAM theorem for systems of infinitely many interacting particles with decaying masses and all-to-all interactions. Using this framework, we construct full-di…
math.DS2026
Robustly transitive behavior in symplectic dynamics
Jaime Paradela
We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a domination condition we…