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Recent Progress on Rigidity Properties of Higher Rank Diagonalizable Actions and Applications

Elon Lindenstrauss

in Dynamics, Geometry, Number Theory: The Impact of Margulis on Modern Mathematics

Published in print:
2022
Published Online:
May 2022
ISBN:
9780226804026
eISBN:
9780226804163
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226804163.003.0012
Subject:
Mathematics, Geometry / Topology

The rigidity properties of higher rank diagonalizable actions is a major theme in homogeneous dynamics, with origins in work of Cassels and Swinnerton-Dyer in the 1950s and Furstenberg. We survey ... More


Classical and quantum ergodicity

Christopher D. Sogge

in Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160757
eISBN:
9781400850549
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160757.003.0006
Subject:
Mathematics, Numerical Analysis

This chapter proves results involving the quantum ergodicity of certain high-frequency eigenfunctions. Ergodic theory originally arose in the work of physicists studying statistical mechanics at the ... More


Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Christopher D. Sogge

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160757
eISBN:
9781400850549
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160757.001.0001
Subject:
Mathematics, Numerical Analysis

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. The book gives a proof of the sharp Weyl ... More


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