Contacto
Mapa del Sitio
buscar
Búsqueda avanzada
FONDECYT-REGULAR - 2001 - 1010447
COMBINATORIAL COMPLEXITY OF ORBITS IN TOPOLOGICAL DYNAMICAL SYSTEMS.
  • Nombre : COMBINATORIAL COMPLEXITY OF ORBITS IN TOPOLOGICAL DYNAMICAL SYSTEMS.
  • Número : 1010447
  • Año Concurso : 2001
  • Concurso : FONDECYT-REGULAR
  • Consejo : CIENCIA
  • Duración : 4 años
  • Estado : APROBADO
  • Sector de Aplicación : CONOCIMIENTO GENERAL

This project concerns the study of aspects of the global behavior of topological dynamical systems which can be deduced from the combinatorial study of their orbits. This point of view is being developed since the introduction of the first combinatorial notions related to the definition of topological entropy and nowadays it appears in different complexity notions associated to topological dynamical systems. The main topics we will consider in this proposal concern the theory of entropy pairs and topological complexity, and Li-Yorke chaos.

The main problems to be studied are:

(1) The gap in the local variational principle: the local variational principle for entropy pairs in [BGH] states that the topological entropy of an open cover is lower or equal to the supremun over all invariant measures of the infimum over all partitions finer than the cover of the measure-theoretical entropy of the partition.
In this proposal we plan to study the gap between the topological entropy of the cover and this second quantity, and try to exhibit nice classes of systems where the gap is zero. In particular we will study this condition for symbolic systems.

(2) Topological entropy using partitions: it is in the aim of this proposal to explore new definitions of topological entropy, only depending on Borel partitions and producing the same set of entropy pairs.

(3) Some problems related with topological and measure-theoretical complexity: state relations between the notions of topological complexity of [BHM] and the measure theoretical complexity of [F1].

(4) Systems without Li--Yorke pairs: we would like to prove a disjointness theorem between minimal systems without Li--Yorke pairs and scattering systems (not only for SPI systems as in [BKM]), to study the same kind of results for minimal systems whose PI towers are made only of asymptotic and isometric extensions.

(5) Positive entropy vs big scrambled sets: in this proposal we plan to pursue our research on the construction of big scrambled sets for positive entropy systems. We will study how the set of entropy pairs could produce a big scrambled set.

(6) Completely scrambled sets: We plan to study the global dynamics of systems such that the whole cartesian product of the systems with itself out of the diagonal is an scrambled set. In particular transitivity properties and topological complexity.

ARTICULOS
  • A NOTE ON LIMIT LAWS FOR MINIMAL CANTOR SYSTEMS WITH INFINITE PERIODIC SPECTRUM, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, VOL.9 (3):745-750, 2003.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • DURAND, FABIEN.




  • CONSTANT-LENGTH SUBSTITUTIONS AND COUNTABLE SCRAMBLED SETS, NONLINEARITY, VOL.17 (3):817-833, 2004.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • BLANCHARD, FRANCOIS
    • DURAND, FABIEN.




  • CONTINUOUS AND MEASURABLE EIGENFUNCTIONS OF LINEARLY RECURRENT DYNAMICAL CANTOR SYSTEMS, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, VOL.67:790-804, 2003.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • CORTEZ MUÑOZ, MARIA ISABEL
    • DURAND, FABIEN
    • HOST, BERNARD.




  • ENTROPY PAIRS AND A LOCAL ABRAMOV FORMULA FOR A MEASURE THEORETICAL ENTROPY OF OPEN COVERS, ERGODIC THEORY AND DYNAMICAL SYSTEMS (PRINT), VOL.24 (4):1127-1153, 2004.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • HUANG, WEN
    • ROMAGNOLI PRADO, PIERRE PAUL
    • YE, XIANDONG.




  • ON LI-YORKE PAIRS, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, VOL.547:51-68, 2002.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • BLANCHARD, FRANCOIS
    • GLASNER, ELI
    • KOLYADA, SERGEI.




  • SEQUENCE ENTROPY PAIRS AND COMPLEXITY PAIRS FOR A MEASURE, ANNALES DE L INSTITUT FOURIER, VOL.54 (4):1005-1028, 2004.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • HUANG, WEN
    • YE, XIANDONG.




CONGRESO
EVENTOS
  • CONTINUOS AND MEASURABLE EIGENVALUES OF MINIMAL CANTOR DYNAMICAL SYSTEMS, En: 14° CONGRESO DE MATEMATICA CAPRICORNIO. ARICA, CHILE. 20040804-20040807.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.




  • DYNAMICS OF EXPANSIVE AND POSITIVELY EXPANSIVE ONE-DIMENSIONAL CELLULAR AUTOMATA, En: 5° REUNION CONJUNTA AMS-SMM. MORELIA, MEXICO. 20010523-20010526.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • BOYLE, MIKE.




  • EIGENVALUES OF LINEARLY RECURRENT CANTOR DYNAMICAL SYSTEMS AND GENERALISATIONS TO SOME TILING SYSTEMS, En: 2004 SPRING MEETING OF THE MARYLAND-PENN STATE WORKSHOP ON DYNAMICAL SYSTEMS AND RELATED TOPICS. WASHINGTON, ESTADOS UNIDOS DE AMERICA. 20040320-20040323.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • BRESSAUD, XABIER
    • DURAND, FABIEN.




  • ITERATIONS OF PROBABILITY MEASURES BY CELLULAR AUTOMATA, En: 2002 INTERNATIONAL WORKSHOP ON CELLULAR AUTOMATA. PRAGA, CHECOSLOVAQUIA. 20020912-20020914.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • MARTINEZ, S.




  • RIGIDITY RESULTS FOR ALGEBRAIC CELLULAR AUTOMATA, En: 31° INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING. FINLANDIA. 20040712-20040716.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • HOST, BERNARD
    • MARTINEZ, S.




  • SEQUENCE AND COMPLEXITY PAIRS FOR A MEASURE, En: 2004 ALGEBRAIC AND TOPOLOGICAL DYNAMICS ACTIVITY MAX-PLANCK INSTITUT FUR MATHEMATIK. BONN, ALEMANIA.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • HUANG, WEN
    • YE, XIANDONG.




  • SEQUENCE ENTROPY PAIRS, En: 2004 WORKSHOP ON DYNAMICAL SYSTEMS. CHILE.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.




INFORME FINAL
  • COMBINATORIAL COMPLEXITY OF ORBITS IN TOPOLOGICAL DYNAMICAL SYSTEMS., 2005. 14 p.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.




MANUSCRITOS
  • NECESSARY AND SUFFICIENT CONDITIONS TO BE AN EIGENVALUE FOR LINEARLY RECURRENT DYNAMICAL CANTOR SYSTEMS, 2005. 26 p.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • BRESSAUD, XABIER
    • DURAND, FABIEN.




  • ROTATION TOPOLOGICAL FACTORS OF MINIMAL ZD-ACTIONS ON THE CANTOR SET, 2005. 9 p.
  • Autores Asociados al Proyecto

    • MAASS SEPULVEDA, ALEJANDRO EDUARDO.


    Autores No Asociados al Proyecto

    • CORTEZ MUÑOZ, MARIA ISABEL
    • GAMBAUDO, JEAN MARC.




TESIS
  • C-ESCRITURAS Y CLASIFICACION POR CONTEXTO, Tesis para optar al grado de M.SC. IN CIENCIAS DE LA COMPUTACION. SANTIAGO, CHILE. UNIVERSIDAD DE CHILE (UCH), FACULTAD DE CIENCIAS FISICAS Y MATEMATICAS, ESCUELA DE POSTGRADO. 2004. 1 p. Profesor Guia: MAASS SEPULVEDA, ALEJANDRO EDUARDO.
  • Autores Asociados al Proyecto



    Autores No Asociados al Proyecto

    • ACUÑA AGUAYO, VICENTE ERNESTO.




CIENCIA, CONOCIMIENTO GENERAL
volver

Comisión Nacional de Investigación Científica y Tecnológica - CONICYT
Canadá 308, Providencia, Santiago de Chile. Teléfono (56 2) 3654400, Fax (56 2) 6551396
Políticas de Privacidad y Condiciones de Uso