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Laurent Niederman (Laboratoire Mathématiques d'Orsay and IMCCE/ASD Orsay, France)04/12/2019, 09:45
We present a survey of stability results for elliptic equilibrium positions in Hamiltonian systems under generic assumptions.
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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.... -
Godofredo Iommi (UC)04/12/2019, 11:10
In the context of countable Markov shifts I will present a result that relates the escape of mass, the measure theoretic entropy and the entropy at infinity of the system. This relation has several consequences. For example, that the entropy map is upper semi-continuous for finite entropy Markov shifts. This is joint work with Mike Todd and Anibal Velozo.
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Sebastián Donoso (U. de Chile)04/12/2019, 11:40
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...
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Mario Ponce (UC)04/12/2019, 12:25
When a group action of positive circle diffeomorphisms is considered, the projective derivative gives raise to a cocycle of M ̈obius transformations. By deducing precise expressions of this cocycle, we obtain several results about reducibility and almost reducibility to the group of rotations SL(2,R). We also discuss novel and classical results about the projective derivative for real maps....
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Anahí Gajardo (U. de Concepción)04/12/2019, 14:30
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.
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In this talk we consider the family of reversible one-way... -
Dante Carrasco (UBB)04/12/2019, 15:00
The notion of expansive homeomorphism is important in topological dynamics,[2]. Different authors have extended some of these notions in more general contexts, in particular the notion of separating theory [1]. In this direction, we show some
basic properties of some levels of separating homeomorphisms since the measurable point of view.Acknowledgement
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The author was partially... -
Carlos Morales ( Universidade Federal do Rio de Janeiro )05/12/2019, 09:30
(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...
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Alejandro Maass (U. de Chile )05/12/2019, 10:55
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,...
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Samuel Petite (Université de Picardie Jules Verne)05/12/2019, 11:25
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
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system that is neither equicontinuous... -
Felipe Riquelme (PUCV)05/12/2019, 12:10
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.
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Salomón Rebollo (UBB)05/12/2019, 14:30
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.
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Leonel Badilla (UBB)05/12/2019, 15:20
Authors: L. BADILLA, D. CARRASCO-OLIVERA, V.F. SIRVENT AND H. VILLAVICENCIO
Abstract: We introduce the definitions of expansivity and topological stability for homeomorphism on fuzzy metric space. We show some basic properties of fuzzy expansive homeomorphisms. Moreover we prove Walters’ theorem in the context of fuzzy metric spaces, i.e., a fuzzy expansive system with the fuzzy shadowing...
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Camilo Lacalle (UBB)05/12/2019, 15:50
In this talk, we consider a class of asymptotically subadditive sequences on countable Markov shifts. This type of sequences appears naturally in the theory of factors of Gibbs measures and also in some dimension problems of non conformal maps.
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We show that the type of sequences we consider
generalizes almost additive sequences under certain finiteness conditions on the space. We define the... -
Radu Saghin (PUCV)06/12/2019, 09:30
We consider a family of area preserving non-invertible maps on the two-torus, which is the composition of the well-known Chirikov standard family ($s_r$) with a linear expansion $E$. If $E$ is an homothety then our family can be seen as a "randomized" version of the standard family. We show on one hand that the Lyapunov exponents are different for all small values of $r$. On the other hand,...
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Rodrigo Torres (UBB)06/12/2019, 10:00
Turing machines have traditionally been studied as computational models, but we center our line of research on the dynamical properties of Turing machines, thus focusing on their behavior rather than the final results. This approach, in the context of Turing machines, has been fruitful since its inception by K ̊urka in 1997 [2], with studies on immortality [4, 5], entropy, equicontinuity,...
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Italo Cipriano (UC)06/12/2019, 11:00
From a dynamical approach, the problem of approximation of integrals with respect to stationary probability measures is analogue to the problem of approximation of integrals with respect to the Lebesgue measure studied by Jenkinson and Pollicott in [”A dynamical approach to accelerating numerical integration with equidistributed points.” Proceedings of the Steklov Institute of Mathematics...
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Moore Ryo (UC)06/12/2019, 11:30
This is a joint work with Zolt\'an Buczolich and Bal\'azs Maga. Let $(\Omega, \sigma)$ be the full-shift of two alphabets, and $f$ be a continuous, real-valued function on it. Let $L_f$ be the set of all of the possible limiting values of the Birkhoff averages of $f$, i.e.
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$$L_f := \left{\alpha \in \mathbb{R} : \exists \, \omega \in \Omega \text{ such that } \lim_{N \to \infty} \frac{1}{N}... -
Carlos Vásquez (PUCV)06/12/2019, 12:15
In 1994, Ittai Kan provided the first examples of maps with intermingled basin. The Kan's example corresponds to a partially hyperbolic endomorphism defined on a surface with boundary exhibiting two intermingled hyperbolic physical measures. Both measures are supported on the boundary and are also measures maximizing the topological entropy. In this talk we will discuss the existence of a...
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Víctor Sirvent (UCN)
For $\beta\in \mathbb{C}$ with $|\beta|<1$ define the contractions
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$h_0(z)=\beta z$ and $h_1(z)=\beta z+1$
and consider the attractor $A_\beta$ of the iterated function system $\{h_0,h_1\}$. In 1985 Barnsley and Harrington introduced the ``Mandelbrot set for pairs of linear maps'' which is the set of all $\beta$ with connected attractor $A_\beta$. This set has been thoroughly studied by...
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