2 citations · 6 across the 12 of their papers we have counts for
13 papers
Rigidity of Mather's -function on a KAM set for analytic billiards-like maps and unique quasi-analytic continuation
Corentin Fierobe, Vadim Kaloshin, Frank Trujillo
In his seminal paper, Kac famously asked whether "one can hear the shape of a drum" - that is whether the isometry class of a bounded domain in a Euclidean space is uniquely determ…
Non-autonomous KAM theory for lower dimensional invariant tori (II): Normally parabolic case
Donato Scarcella, Frank Trujillo
Dynamical systems subject to non-autonomous perturbations decaying in time arise naturally in many physical contexts, including laser-molecule interactions, epidemiological models,…
Non-autonomous KAM theory for lower dimensional invariant tori (I): Normally elliptic and hyperbolic cases
Donato Scarcella, Frank Trujillo
Many physical phenomena are naturally modeled by dynamical systems subject to non-autonomous perturbations that decay in time, including the interaction of a laser pulse with a mol…
On the ergodicity of infinite antisymmetric extensions of symmetric IETs
Przemysław Berk, Frank Trujillo
In this article, we consider skew product extensions over symmetric interval exchange transformations with respect to the cocycle . More precisely, we…
On the Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms
Frank Trujillo
We show that, generically, the unique invariant measure of a sufficiently regular piecewise smooth circle homeomorphism with irrational rotation number and zero mean nonlinearity (…
Ergodicity of explicit logarithmic cocycles over IETs
Przemysław Berk, Frank Trujillo, Corinna Ulcigrai
We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, gives explicit…
Affine IETs with a singular conjugacy to an IET
Frank Trujillo, Corinna Ulcigrai
We produce affine interval exchange transformations (AIETs) which are topologically conjugated to (standard) interval exchange maps (IETs) via a singular conjugacy, i.e. a diffeomo…
Periodic and chaotic dynamics in a map-based neuron model
Frank Llovera Trujillo, Justyna Signerska-Rynkowska, Piotr Bartłomiejczyk
Map-based neuron models are an important tool in modelling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on con…
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…
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…
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…
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…
On the Hausdorff dimension of invariant measures for multicritical circle maps
Frank Trujillo
We give explicit bounds for the Hausdorff dimension of the unique invariant measure of multicritical circle maps without periodic points. These bounds depend only on the arit…