Monodromy representations and Lyapunov exponents of origamis
Origamis are translation surfaces obtained by gluing finitely many unit squares and provide an easy access to Teichmüller curves. In particular, their monodromy represenation can be explicitely determined. A general principle for the decomposition of this represenation is exhibited and applied to ex...
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| Format: | Online |
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KIT Scientific Publishing
2021
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| _version_ | 1869529831886028800 |
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| author | Kappes, André |
| author_browse | Kappes, André |
| author_facet | Kappes, André |
| author_sort | Kappes, André |
| collection | Directory of Open Access Books |
| description | Origamis are translation surfaces obtained by gluing finitely many unit squares and provide an easy access to Teichmüller curves. In particular, their monodromy represenation can be explicitely determined. A general principle for the decomposition of this represenation is exhibited and applied to examples. Closely connected to it is a dynamical cocycle on the Teichmüller curve. It is shown that its Lyapunov exponents, otherwise inaccessible, can be computed for a subrepresentation of rank two. |
| format | Online |
| id | doab-20.500.12854ir-53916 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | KIT Scientific Publishing |
| publisherStr | KIT Scientific Publishing |
| record_format | ojs |
| spelling | doab-20.500.12854ir-539162023-12-20T18:40:37Z Monodromy representations and Lyapunov exponents of origamis Kappes, André QA1-939 variation of Hodge structures Lyapunov exponent square-tiled surface Kontsevich-Zorich cocycle Teichmüller curve Veech group bic Book Industry Communication::P Mathematics & science Origamis are translation surfaces obtained by gluing finitely many unit squares and provide an easy access to Teichmüller curves. In particular, their monodromy represenation can be explicitely determined. A general principle for the decomposition of this represenation is exhibited and applied to examples. Closely connected to it is a dynamical cocycle on the Teichmüller curve. It is shown that its Lyapunov exponents, otherwise inaccessible, can be computed for a subrepresentation of rank two. 2021-02-11T20:08:23Z 2021-02-11T20:08:23Z 2019-07-30 20:02:00 2011 book 35222 9783866447516 https://directory.doabooks.org/handle/20.500.12854/53916 eng image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://www.ksp.kit.edu/9783866447516 KIT Scientific Publishing 10.5445/KSP/1000024418 10.5445/KSP/1000024418 68fffc18-8f7b-44fa-ac7e-0b7d7d979bd2 9783866447516 VIII, 138 p. open access |
| spellingShingle | QA1-939 variation of Hodge structures Lyapunov exponent square-tiled surface Kontsevich-Zorich cocycle Teichmüller curve Veech group bic Book Industry Communication::P Mathematics & science Kappes, André Monodromy representations and Lyapunov exponents of origamis |
| title | Monodromy representations and Lyapunov exponents of origamis |
| title_full | Monodromy representations and Lyapunov exponents of origamis |
| title_fullStr | Monodromy representations and Lyapunov exponents of origamis |
| title_full_unstemmed | Monodromy representations and Lyapunov exponents of origamis |
| title_short | Monodromy representations and Lyapunov exponents of origamis |
| title_sort | monodromy representations and lyapunov exponents of origamis |
| topic | QA1-939 variation of Hodge structures Lyapunov exponent square-tiled surface Kontsevich-Zorich cocycle Teichmüller curve Veech group bic Book Industry Communication::P Mathematics & science |
| topic_facet | QA1-939 variation of Hodge structures Lyapunov exponent square-tiled surface Kontsevich-Zorich cocycle Teichmüller curve Veech group bic Book Industry Communication::P Mathematics & science |
| url | 35222 |
| work_keys_str_mv | AT kappesandre monodromyrepresentationsandlyapunovexponentsoforigamis |