Ergodic Theory and Negative Curvature

Released on by Boris Hasselblatt
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  • Ergodic Theory and Negative Curvature Book Detail

  • Author : Boris Hasselblatt
  • Release Date : 2017-12-15
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 334
  • ISBN 13 : 3319430599
  • File Size : 66,66 MB
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Ergodic Theory and Negative Curvature by Boris Hasselblatt PDF Summary

Book Description: Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study. The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.

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Ergodic Theory and Negative Curvature

Ergodic Theory and Negative Curvature

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Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are

The Ergodic Theory of Discrete Groups

The Ergodic Theory of Discrete Groups

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The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. The