Dynamics and Randomness

1. Front Matter

   Pages i-vii

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2. Dimension-Like Characteristics of Invariant Sets in Dynamical Systems

   • Valentin Afraimovich, Jesus Urias

   Pages 1-30

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3. Positive K-Theory and Symbolic Dynamics

   • Mike Boyle

   Pages 31-52

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4. Combinatorial and Dynamical Study of Substitutions Around the Theorem of Cobham

   • Fabien Durand

   Pages 53-94

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5. Irreducibility, Homoclinic Points and Adjoint Actions of Algebraic ℤ^d-Actions of Rank One

   • Manfred Einsiedler, Klaus Schmidt

   Pages 95-124

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6. Old and New Tools in the Theory of Filtrations

   • Émery Michel

   Pages 125-146

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7. Information Compression and Retention in Dynamical Processes

   • Karl Petersen

   Pages 147-217

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8. Unique Equilibrium States

   • Robert R. Phelps

   Pages 219-225

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9. Poincare Inequalities and Spectral Gap, Concentration Phenomenon for G-Measures

   • Bernard Schmitt

   Pages 227-273

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10. Back Matter

    Pages 275-275

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This book contains the lectures given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile from December 11th to 15th, 2000. This meeting brought together mathematicians, theoretical physicists and theoretical computer scientists, and graduate students interested in fields re­ lated to probability theory, ergodic theory, symbolic and topological dynam­ ics. We would like to express our gratitude to all the participants of the con­ ference and to the people who contributed to its organization. In particular, to Pierre Collet, Bernard Host and Mike Keane for their scientific advise. VVe want to thank especially the authors of each chapter for their well­ prepared manuscripts and the stimulating conferences they gave at Santiago. We are also indebted to our sponsors and supporting institutions, whose interest and help was essential to organize this meeting: ECOS-CONICYT, FONDAP Program in Applied Mathematics, French Cooperation, Fundacion Andes, Presidential Fellowship and Universidad de Chile. We are grateful to Ms. Gladys Cavallone for their excellent work during the preparation of the meeting as well as for the considerable task of unifying the typography of the different chapters of this book.

• Measure
• Probability theory
• Statistical Physics
• Symbol
• coding
• coding theory
• computer
• filtration
• information
• information theory
• stochastic process

• Department of Mathematical Engineering, Faculty of Physical and Mathematical Sciences, University of Chile, Santiago, Chile

  Alejandro Maass, Servet Martínez, Jaime San Martín

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