Open problems in dynamics and related fields
type: Item
instance of: scholarly article
title: Open problems in dynamics and related fields
zbMATH Open document ID: 1118.37002
author: Alexander Gorodnik
published in: Journal of Modern Dynamics
publication date: 2007-04-10T00:00:00Z
review text: 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.
reviewed by: Ranjeet Sehmi
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 11Jxx
Mathematics Subject Classification ID: 11Gxx
Mathematics Subject Classification ID: 22-02
Mathematics Subject Classification ID: 81Q50
zbMATH DE Number: 5141223
zbMATH Keywords: André Oort conjecture
zbMATH Keywords: arithmetic groups
zbMATH Keywords: Diophantine approximation
zbMATH Keywords: divergent orbits
zbMATH Keywords: equidistribution
zbMATH Keywords: global rigidity
zbMATH Keywords: local rigidity
zbMATH Keywords: Littlewood conjecture
zbMATH Keywords: measure rigidity
zbMATH Keywords: polygonal billiards
zbMATH Keywords: quantum chaos
zbMATH Keywords: symbolic coding
MaRDI profile type: Publication
full work available at URL: jmd.2007.1.1
OpenAlex ID: W1992532192
DOI: 10.3934/JMD.2007.1.1
description: scientific article; zbMATH DE number 5141223