| 000 | 02508nam a22002897a 4500 | ||
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| 003 | NISER | ||
| 005 | 20260305095359.0 | ||
| 008 | 260303b |||||||| |||| 00| 0 hin d | ||
| 020 |
_a9788195782949 _qPaperback |
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| 040 |
_aNISER LIBRARY _beng _cNISER LIBRARY |
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| 082 | 0 | 4 |
_a514.12 _bATH-T |
| 100 | 1 | _aAthreya, Jayadev S. | |
| 245 | 1 | 0 | _aTranslation surfaces |
| 260 |
_aNew Delhi : _bHindustan Book Agency, _c2024. |
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| 300 | _axi, 179 pages. | ||
| 490 |
_aTexts and readings in mathematics ; _v87 |
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| 504 | _aIncludes bibliographical references and index. | ||
| 520 | _aThis textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting prob- lems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmüller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial. | ||
| 650 | 0 | _aTranslation surfaces | |
| 650 | 0 | _aRiemann surfaces | |
| 650 | 0 |
_aDynamical systems and ergodic theory _xErgodicity, mixing, rates of mixing. |
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| 650 | 0 | _aErgodic theory | |
| 700 | 1 | _aMasur, Howard | |
| 856 | 4 | 1 |
_3Table of contents _uhttps://www.hindbook.com/images/trim87_content.pdf |
| 856 | 4 | 1 |
_3Reviews _uhttps://www.goodreads.com/book/show/212388942-translation-surfaces?ref=nav_sb_ss_1_13#CommunityReviews |
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_c36839 _d36839 |
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