Iosif Polterovich's Books

Topics in Spectral Geometry

By: Michael Levitin,Dan Mangoubi,Iosif Polterovich

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Topics in Spectral Geometry

By: Michael Levitin,Dan Mangoubi,Iosif Polterovich

It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question “Can one hear the shape of a drum?” In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites.

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Page Count

346

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470475480

ISBN 13

9781470475482

Spectrum and Dynamics

Proceedings of the Workshop Held in Montreal, QC, April 7--11, 2008

By: Dmitry Jakobson,Stephane Nonnenmacher,Iosif Polterovich

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Spectrum and Dynamics

Proceedings of the Workshop Held in Montreal, QC, April 7--11, 2008

By: Dmitry Jakobson,Stephane Nonnenmacher,Iosif Polterovich

This volume contains a collection of papers presented at the workshop on Spectrum and Dynamics held at the CRM in April 2008. In recent years. many new exciting connections have been established between the spectral theory of elliptic operators and the theory of dynamical systems. A number of articles in the proceedings highlight these discoveries. The volume features a diversity of topics. Such as quantum chaos, spectral geometry. Semiclassical analysis, number theory and ergodic theory. Apart from the research papers aimed at the experts, this book includes several survey articles accessible to a broad math ematical audience.

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