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28. Bi-rational maps in four dimensions with two invariants

Author

Nalini Joshi, Giorgio Gubbiotti, Claude-Michel Viallet, Dinh T. Tran, Paris-Centre de Recherche Cardiovasculaire (PARCC - UMR-S U970), Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Hôpital Européen Georges Pompidou [APHP] (HEGP), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpitaux Universitaires Paris Ouest - Hôpitaux Universitaires Île de France Ouest (HUPO)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpitaux Universitaires Paris Ouest - Hôpitaux Universitaires Île de France Ouest (HUPO), Laboratoire de Physique Théorique et Hautes Energies (LPTHE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Viallet, Claude, Université Paris Descartes - Paris 5 (UPD5)-Hôpital Européen Georges Pompidou [APHP] (HEGP), Hôpitaux Universitaires Paris Ouest - Hôpitaux Universitaires Île de France Ouest (HUPO)-Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Hôpitaux Universitaires Paris Ouest - Hôpitaux Universitaires Île de France Ouest (HUPO)-Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Institut National de la Santé et de la Recherche Médicale (INSERM), Gubbiotti, G., Joshi, N., Tran, D. T., and Viallet, C. -M.

Subjects
Statistics and Probability, Inflation, Pure mathematics, Class (set theory), algebraic entropy, media_common.quotation_subject, FOS: Physical sciences, General Physics and Astronomy, [MATH] Mathematics [math], integrability, 01 natural sciences, [PHYS] Physics [physics], 0103 physical sciences, [NLIN] Nonlinear Sciences [physics], Point (geometry), [NLIN]Nonlinear Sciences [physics], inflation, [MATH]Mathematics [math], 0101 mathematics, Mathematical Physics, Mathematics, media_common, [PHYS]Physics [physics], Nonlinear Sciences - Exactly Solvable and Integrable Systems, Degree (graph theory), Liouville integrability, bi-rational map, 010102 general mathematics, difference equation, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), 37F10, 37J15, 39A10, Modeling and Simulation, 010307 mathematical physics, Exactly Solvable and Integrable Systems (nlin.SI)
Abstract

In this paper we present a class of four-dimensional bi-rational maps with two invariants satisfying certain constraints on degrees. We discuss the integrability properties of these maps from the point of view of degree growth and Liouville integrability., 26 pages. arXiv admin note: text overlap with arXiv:1808.04942

Published
2020
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