A Survey of Some Arithmetic Applications of Ergodic Theory in Negative Curvature
Parkkonen, J., & Paulin, F. (2017). A Survey of Some Arithmetic Applications of Ergodic Theory in Negative Curvature. In B. Hasselblatt (Ed.), Ergodic Theory and Negative Curvature : CIRM Jean-Morlet Chair, Fall 2013 (pp. 293-326). Lecture Notes in Mathematics, 2164. Springer International Publishing. doi:10.1007/978-3-319-43059-1_7
Published inLecture Notes in Mathematics
© Springer International Publishing Switzerland 2017
This paper is a survey of some arithmetic applications of techniques in the geometry and ergodic theory of negatively curved Riemannian manifolds, focusing on the joint works of the authors. We describe Diophantine approximation results of real numbers by quadratic irrational ones, and we discuss various results on the equidistribution in R , C and in the Heisenberg groups of arithmetically defined points. We explain how these results are consequences of equidistribution and counting properties of common perpendiculars between locally convex subsets in negatively curved orbifolds, proven using dynamical and ergodic properties of their geodesic flows. This exposition is based on lectures at the conference “Chaire Jean Morlet: Géométrie et systèmes dynamiques”, at the CIRM, Luminy, 2014. We thank B. Hasselblatt for his strong encouragements to write this survey.
PublisherSpringer International Publishing
Parent publication ISBN978-3-319-43058-4
Is part of publicationErgodic Theory and Negative Curvature : CIRM Jean-Morlet Chair, Fall 2013
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