We present a survey of stability results for elliptic equilibrium positions in Hamiltonian systems under generic assumptions.
References:
Giorgilli, A., Delshams, A., Fontich, E., Galgani, L., and Simo, C., Effective Stability for a Hamiltonian System near an Elliptic Equilibrium Point, with an Application to the Restricted Three-Body Problem, J. Differential Equations, 1989, vol. 77, no....
In this talk I will review the notion of joint ergodicity in the context of multiple ergodic averages. Essentially, this property says that a multiple average converges to the ‘’correct’’ limit, namely a product of integrals. This property was discovered by Furstenberg for linear iterates in weakly mixing systems and extended for polynomials (also in weakly mixing systems) by Bergelson. When...
In the context of Cellular Automata (CA), "pre-expansivity" is the property of being positively expansive on asymptotic pairs of configurations (i. e. configurations that differ in only finitely many positions). Pre-expansivity therefore lies between positive expansivity and pre-injectivity, two important notions of CA theory.
In this talk we consider the family of reversible one-way...
(joint with X. Wen and Y. Yang) A new kind of expansiveness for flows namely the singular-expansivity is proposed. We prove that it coincides with the rescaling expansivity for C1 generic vector fields. We give sufficient conditions for a k*-expansive flow to be singular-expansive. We prove that a singular-expansive flow has countably many periodic orbits and, if the set of singularities is...
In this talk we will discuss about the dynamics of topological finite rank systems. This class of Cantor systems arise naturally in symbolic dynamics and also in the study of interval exchange maps. It is an extension of the so called substitution systems and linearly recurrent. Surprisingly, many dynamical properties of this last systems can be extended to topological finite rank systems,...
A minimal Cantor system is said to be self-induced whenever it is conjugate to one of its induced systems. Substitution subshifts and some odometers are classical examples, in a common work with F. Durand and N. Ormes, we show that these are the only examples in the equicontinuous or expansive case. Nevertheless, we exhibit a zero entropy self-induced
system that is neither equicontinuous...
In this talk we discuss the existence of maximizing measures for uniformly continuous potentials on negatively curved non-compact manifolds. This is a joint work with Aníbal Velozo.
We will show how limit cycles, which form part of a dynamic object: an ordinary differential equation, are related with zeros of an analytic object: an Abelian integral. We will show when such a relation is an equivalence and we will exhibit some recent results about these two objects.
