Dynamics of the ultra-discrete Toda lattice via Pitman's transformation (Mathematical structures of integrable systems and their applications)
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- Croydon, David A.
- Research Institute for Mathematical Sciences, Kyoto University
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- 佐々田, 槙子
- Graduate School of Mathematical Sciences, University of Tokyo
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- 辻本, 諭
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University
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By encoding configurations of the ultra-discrete Toda lattice by piecewise linear paths whose gradient alternates between -1 and 1, we show that the dynamics of the system can be described in terms of a shifted version of Pitman's transformation (that is, reflection in the past maximum of the path encoding). This characterisation of the dynamics applies to finite configurations in both the non-periodic and periodic cases, and also admits an extension to infinite configurations. The latter point is important in the study of invariant measures for the ultra-discrete Toda lattice, which is pursued in the parallel work [3]. We also describe a generalisation of the result to a continuous version of the box-ball system, whose states are described by continuous functions whose gradient may take values other than ±1.
"Mathematical structures of integrable systems and their applications". September 5-7, 2018. edited by Shinsuke Iwao. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.
収録刊行物
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- 数理解析研究所講究録別冊
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数理解析研究所講究録別冊 B78 235-250, 2020-04
Research Institute for Mathematical Sciences, Kyoto University
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詳細情報 詳細情報について
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- CRID
- 1050850634912190464
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- NII論文ID
- 120006950553
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- NII書誌ID
- AA12196120
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- ISSN
- 18816193
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- HANDLE
- 2433/260639
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- 本文言語コード
- en
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- 資料種別
- departmental bulletin paper
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- IRDB
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