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A classification of two dimensional integrable mappings and rational elliptic surfaces

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Title: A classification of two dimensional integrable mappings and rational elliptic surfaces
Authors: Carstea, A. S., Takenawa, T.
Publication Year: 2010
Collection: Mathematics
Nonlinear Sciences
Subject Terms: Mathematics - Dynamical Systems, Mathematics - Algebraic Geometry, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 14H70
More Details: We classify two dimensional integrable mappings by investigating the actions on the fiber space of rational elliptic surfaces. While the QRT mappings can be restricted on each fiber, there exist several classes of integrable mappings which exchange fibers. We also show an equivalent condition when a generalized Halphen surface becomes a Halphen surface of index m.
Comment: 22 pages, 6 figures
Document Type: Working Paper
Access URL: http://arxiv.org/abs/1005.3586
Accession Number: edsarx.1005.3586
Database: arXiv
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  Data: A classification of two dimensional integrable mappings and rational elliptic surfaces
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  Data: 2010
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  Data: Mathematics<br />Nonlinear Sciences
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  Data: We classify two dimensional integrable mappings by investigating the actions on the fiber space of rational elliptic surfaces. While the QRT mappings can be restricted on each fiber, there exist several classes of integrable mappings which exchange fibers. We also show an equivalent condition when a generalized Halphen surface becomes a Halphen surface of index m.<br />Comment: 22 pages, 6 figures
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      – SubjectFull: Mathematics - Dynamical Systems
        Type: general
      – SubjectFull: Mathematics - Algebraic Geometry
        Type: general
      – SubjectFull: Nonlinear Sciences - Exactly Solvable and Integrable Systems
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      – TitleFull: A classification of two dimensional integrable mappings and rational elliptic surfaces
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