A new class of integrable maps of the plane: Manin transformations with involution curves

DOI10.3842/SIGMA.2021.067zbMath1473.14024arXiv2009.09854MaRDI QIDQ2236607

Peter H. van der Kamp

Publication date: 25 October 2021

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.09854

zbMATH Keywords

invariantManin transformationBertini involutionintegrable map of the planepencil of cubic curves

Mathematics Subject Classification ID

Relationships between algebraic curves and integrable systems (14H70) Rational and birational maps (14E05) Lattice dynamics; integrable lattice equations (37K60) Completely integrable discrete dynamical systems (37J70)

Uses Software

• Maple

Cites Work

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• Manin involutions for elliptic pencils and discrete integrable systems
• Integrable mappings and soliton equations
• Integrable mappings and soliton equations. II
• Generalised Manin transformations and QRT maps
• Dynamics of bimeromorphic maps of surfaces
• Discrete Systems and Integrability
• The staircase method: integrals for periodic reductions of integrable lattice equations
• An algebraic geometric approach to integrable maps of the plane
• Integrable maps
• Integrable mappings of the plane preserving biquadratic invariant curves II
• Integrable mappings via rational elliptic surfaces
• Integrable Boundary Conditions for Quad Equations, Open Boundary Reductions, and Integrable Mappings
• Notes on the Bertini involution
• Birational involutions of \({\mathbb{P}}^ 2\).

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