Journal of Modern Dynamics (JMD)

Open problems in dynamics and related fields

Pages: 1 - 35, Issue 1, January 2007      doi:10.3934/jmd.2007.1.1

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Alexander Gorodnik - 172 Sloan, Caltech, Pasadena, CA 91125, United States (email)

Abstract: The paper discusses a number of open questions,which were collected during the AIM workshop “Emerging applications of measure rigidity”. The main emphasis is made on the rigidity problems in the theory of dynamical systems and their connections with Diophantine approximation, arithmetic geometry, and quantum chaos.

Keywords:  André-Oort conjecture, arithmetic groups, Diophantine approximation, divergent orbits, equidistribution, global rigidity, local rigidity, Littlewood conjecture, measure rigidity, polygonal billiards, quantumchaos, symbolic coding.
Mathematics Subject Classification:  Primary: 37-02; Secondary: 11-02, 14-02, 81-02.

Received: March 2006;      Revised: April 2006;      Available Online: October 2006.