Dynamical Systems and Diophantine Approximation
Résumé
On the 7th, 8th and 9th June 2004 has been held at the Institut Henri Poincaré a conference on ''Dynamical systems and Diophantine approximation''. One of the aims of this conference was to give a survey of research tools at the interface between these two domains. Our goal was also to highlight methods and open questions. The proceedings we are presenting in this volume reflect the spirit of this congress. The reader will find surveys and articles on the convergence or divergence points between dynamical systems and Diophantine approximation. All these text are written to be accessible to a wide audience.
Mots clés
Transfer operator
product of random stationary matrices
Lyapunov spectrum
Jacobi-Perron algorithm
multidimensional continued fractions algorithm
simultaneous Diophantine approximation
Hausdorff dimension
locally symmetric space
unipotent flow
Ratner's theorem
p-adic homogeneous space
orbit closure
Heegner points
polygonal billiards