4 papers
math.DS2021
Surviving Lower Dimensional Invariant Tori of a Resonant Torus with any Number of Resonances
Frank Trujillo
We provide sufficient conditions on integrable analytic Hamiltonians that guarantee the existence, under arbitrary sufficiently small analytic perturbations, of invariant lower dim…
math.DS2019
Smooth mixing transformations with loosely Bernoulli cartesian product
Frank Trujillo
A zero-entropy system is said to be loosely Bernoulli if it can be induced from an irrational rotation of the circle. We provide a criterion for zero-entropy systems to be loosely…
math.DS2019
Quasi-analytic properties of the KAM curve
Frank Trujillo
Classical KAM theory guarantees the existence of a positive measure set of invariant tori for sufficiently smooth non-degenerate near-integrable systems. When seen as a function of…
math.DS2019
Lyapunov instability in KAM stable Hamiltonians with two degrees of freedom
Frank Trujillo
For a fixed frequency vector obeying we show the existence of Gevrey-smooth Hamiltonians, arbitrarily close to a…