Open problems in dynamics and related fields
This paper contains a collection of open problems from the workshop ``Emerging applications of measure rigidity'' held at the American Institute of Mathematics in June, 2004. The main emphasis is made on the rigidity problems in the theory of dynamical systems and their connections with Diophantine approximation, arithmetic geometry and mathematical physics. The current status of the problems as well as related references have also been included in the paper. There are in all 58 Conjectures and 59 Questions. The reader is referred to the paper of \textit{B. Hasselblatt} for a collection of interesting open problems based on the 2004 workshop ``Recent progress in dynamics'' in Dynamics, ergodic theory and geometry, Cambridge Univ. Press, to appear]. Contents: 1. Local rigidity; 2. Global rigidity; 3. Measure rigidity; 4. Equidistribution; 5. Divergent trajectories; 6. Symbolic coding; 7. Polygonal billiards; 8. Arithmeticity; 9. Diophantine analysis; 10. Quantum ergodicity and quantum chaos; 11. Andre-Oort conjecture; References.
scientific article; zbMATH DE number 5141223