Seminario de Sistemas Dinámicos

El Seminario de Sistemas Dinámicos de Santiago es el encuentro semanal de matemáticas con mayor tradición en el país pues se realiza ininterrumpidamente desde la década del '80. Se realiza alternadamente en alguna de las instituciones de Santiago donde hay miembros del grupo de Sistemas Dinámicos. Participan así las universidades de Chile, de Santiago, Andrés Bello y Católica de Chile.

 
2009-03-23
Pär Kurlberg. Kth
Introduction to quantum ergodicity and arithmetic quantum maps
Auditorio Ninoslav Bralic - Fcultad de Matemáticas
Abstract:
The quantum mechanical counterpart to classical ergodicity is that
eigenfunctions of the quantized Hamiltonian (stationary states) should
be equidistributed in a certain sense. If a dynamical system is
classically ergodic, Schnirelman´s theorem asserts that most
stationary states are equidistributed. However, subsequences of
exceptional eigenfunctions (scars) cannot be ruled out. On the other
hand, for some systems it seems reasonable to expect that no
exceptional eigenfunctions exist, so called Quantum Unique Ergodicity
(QUE). Other expected consequences of classical chaos is that the
value distribution of eigenfunctions, as well as the value
distribution of matrix coefficients of observables, should be
Gaussian.
2009-03-06
Renaud Leplaideur. Université de Brest
Renormalization and virtual Manneville-Pomeau maps
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:
"
2009-01-26
Yoshifumi Matsuda. Universidad de Tokyo
The Rotation Number Function on Groups of Real-Analytic Diffeomorphisms of The Circle
Fac. de Ciencias de la U. de Chile (Las Palmeras) - 16:30 Hrs.
2009-01-19
Karl Petersen. (Unc)
Sturmian and adic symbolic dynamics from the Farey-Stern-Brocot diagram.
CMM - SALA PISO 7 - 17:00 a 18:00 Hrs.
Abstract:
Abstract: A slight modification of the Farey or Stern-Brocot tree produces a Bratteli diagram and therefore an associated  Bratteli-Vershik adic dynamical system. All Sturmian systems
shows us the lexicographically minimal sequences in Sturmian
lexicographic order of 0,1 sequences here and in beta-shifts,
properties appears.
2009-01-19
Pascale Roesch. U. de Toulouse, Francia
The Boundary of Bounded Polynomial Fatou Components
CMM - SALA PISO 7 - 15:30 a 16:30 Hrs.
2008-12-22
Gabriela Fernández. Impa, Brasil
Flujos Holomorfos Dicríticos en Superficies de Stein
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:

Estudiaremos la clasificación del par (

M,X) donde M es una superficie de Stein y X un campo vectorial holomorfo completo en M. Mostraremos que si M es un superficie con H2(M, Z) = 0 y X tiene una singularidad dicríptica, entonces M es biholomorfa a C2 y el campo X es globalmente linearizable."
2008-12-01
Fabien Duran. Université de Picardie
Rauzy fractal in $R imes C$.
USACH - Sala por confirmar
Abstract:
Abstract: The Rauzy fractal is a well-known object living in $C$ carrying a lot of questions/problems in number theory, dynamical systems, numeration
systems, automata theory, hausdorff dimension, tilings, etc ...
Almost nothing is known for such object in $R imes C$.
We will present some first results in this direction. More specifically,
we will look at the Rauzy fractal generated by the polynomial
P(x)=x4-x3-x2-x-1.
"
2008-11-21
Neil Dobbs. Kth
Hyperbolic Dimension for Interval Maps
Sala N-31 Campus San Joaquín - UC
Abstract:
Abstract: The hyperbolic and Hausdorff dimensions are shown to coincide for $C2$ maps without recurrent critical points. The maps
may have parabolic periodic points. The Julia set for certain such maps may have hyperbolic dimension equal to 1 but Lebesgue measure
equal to 0.
2008-11-17
Alvaro Castañeda. Universidad de Santiago de Chile
Conjetura de Markus-Yamabe para campos vectoriales polinomiales en $R3$
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:

"
2008-11-10
Christophe Dupont. Université Paris Xi
An introduction to the dynamics of holomorphic endomorphisms of
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:

			
						
			

				

			2008-10-27				

				

					Adam Clay. Univ. British Columbia, Vancouver, Canada
Limit Points in Spaces of Group Orderings
 Sala de Seminarios - Departamento de Matemáticas - Universidad de Chile (Las Palmeras) - 16:30 Hrs.				

			

			

			
						
			

				

			2008-10-13				

				

					María Isabel Cortez. Universidad de Santiago de Chile
Realization of a Choquet Simplex as the Set of Invariant Probability Measures of a Postcritical Set
 Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30  Hrs.
Abstract:
Abstract:  In this talk we will show that any Choquet simplex can be seen as the set of invariant probability measures of the restriction of a unimodal map to the omega-limit set of its critical point.    We will present some basic concepts on the dimension group associated to an homeomorphism on the Cantor set,  in order to ask the question if any orbit equivalence class can be realized between the class of postcritical sets.  Joint work with Juan Rivera-Letelier.				

			

			

			
						
			

				

			2008-09-29				

				

					Mike Todd. Universidade Do Porto, Portugal
Lyapunov spectra for multimodal maps
 Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:
Resumen:  A dynamical system can be broken down into sets with the same asymptotic growth.   Analysis of these sets provides a characterisation of the system.  In this talk I will give recent results on the analysis of such sets for multimodal maps of the interval.  I will focus on the interesting way these sets change when we look at maps which are less and less hyperbolic.				

			

			

			
						
			

				

			2008-09-22				

				

					Martín Sambarino. U. de  la República (Uruguay)
Clases Homoclinicas Con Interior No Vacio
 Sala de Seminarios - Departamento de Matemáticas - USACH - 16:30 Hrs.				

			

			

			
						
			

				

			2008-09-08				

				

					Richard Urzúa. Universidad Católica del Norte
Free Smooth $Z^p$-Actions on The Three Torus Dimensional
 Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.				

			

			

			
						
			

				

			2008-08-25				

				

					Daniel Pons. U. Andrés Bello
Generating Simplicial Complexes.
 Sala de Seminarios Física - USACH
Abstract:
Resumen: In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For expansive systems remarkable properties are observed. Known examples are revisited and new examples are presented. This work is a collaboration with P.P.Romagnoli."				

			

			

			
						
			

				

			2008-08-18				

				

					Nuno Luzia. Instituto Superior Técnico, Lisboa.
Hausdorff dimension of Sierpinski sponges.
 Por confirmar: Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:
Resumen: The computation of Hausdorff dimension of fractals generated by a 1-dimensional expanding map is well Known via the famous Moran formula and, more generally, Bowen´s equation in terms of the Pressure function. For fractals generated by 2 or 3-dimensional maps this problem turns out to be more difficult due to the existence of several Lyapunov exponents. We say how to compute the Hausdorff dimension for a class of fractals generalizing the famous Sierpinski carpets and Menger sponges.
 

 
"				

			

			

			
						
			

				

			2008-08-11				

				

					Mariusz Urbanski. U. North Texas.
The Transfinite Hausdorff Dimension
 Auditorio Ninoslav Bralic -16:30 Hrs
Abstract:
Resumen: The transfinite Hausdorff dimension will be introduced. Its
 basic properties, including monotone dimension theorem, intermediate
 dimension theorem, and invariance under bi-Lipschitz maps will be
 discussed. For every ordinal number $alpha $X_alpha$ homeomorphic to the Cantor set (so, of topological zero), will
 be constructed, whose transfinite Hausdorff dimension is equal to $alpha$."				

			

			

			
						
			

				

			2008-08-04				

				

					Eduardo Jorquera. Universidad de Chile
La entropía para acciones de grupos en el circulo
 Sala de Seminarios - Departamento de Matemáticas - Universidad de Chile (Las Palmeras) - 16:30 Hrs
Abstract:
Resumen:  En esta exposición consideraremos un grupo finitamente generado de homeomorfismos del círculo, definiremos de manera natural la entropía y el conjunto de puntos no errantes para la acción de este grupo generalizando la definición clásica para una transformación, y nuestro objetivo sera establecer bajo que hipótesis algebraica o de regularidad tendremos la igualdad entre la entropía de la acción en todo el círculo con la entropía de la acción en el conjunto de puntos no errantes tal como se tiene en el caso clásico de una transformación. 
				

			

			

			
						
			

				

			2008-06-16				

				

					Carlos Vásquez. Universidad Católica de Valparaíso
$u$-medidas con exponentes de Lyapunov centrales positivos.
 Sala de seminarios CMM - Universidad de Chile- 17:00 Hrs
Abstract:
Resumen: 
 
 Consideramos $C^r$-difeomorfimos $f::: M o M$, $r>1$, que poseen un atractor parcialmente hiperbólico $Lambda$ con una descomposición no trivial del fibrado tangente: $T_Lambda M=E^soplusE^coplus E^u$, con $dim E^* e 0$, $*=s,c,u$. 
 En esta exposición discutiremos cuando una $u$-medida con exponente de Lyapunov central positivo es una medida SRB (su bacia métrica tiene medida de Lebesgue positiva) y discutiremos la estabilidad ergodica respecto a esta medida natural.