The group of symplectic birational maps of the plane and the dynamics of a family of 4D maps

DOI10.3934/jgm.2020010zbMath1456.53066OpenAlexW3011838989MaRDI QIDQ2220261

Inês Cruz, Helena Mena-Matos, Esmeralda Sousa-Dias

Publication date: 22 January 2021

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jgm.2020010

zbMATH Keywords

Poisson manifoldssymplectic foliationbirational mapsglobal periodicity

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Rational and birational maps (14E05) Foliations in differential topology; geometric theory (57R30) Multiplicative and other generalized difference equations (39A20) Cluster algebras (13F60) Symplectic and canonical mappings (37J11) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06)

Cites Work

• Lecture notes on cluster algebras
• Discrete integrable systems and Poisson algebras from cluster maps
• Symplectic maps from cluster algebras
• Dynamics of the birational maps arising from \(F_0\) and \(dP_3\) quivers
• Cluster mutation-periodic quivers and associated Laurent sequences
• Multiple reductions, foliations and the dynamics of cluster maps
• Symplectic birational transformations of the plane
• Reduction of cluster iteration maps
• Cluster algebras I: Foundations
• Unnamed Item

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