A Darboux-type Theory of Integrability for Discrete Dynamical Systems

DOI10.1080/1023619021000054042zbMath1013.39008OpenAlexW2060123270MaRDI QIDQ4787670

Víctor Mañosa, Armengol Gasull

Publication date: 20 June 2003

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/1023619021000054042

zbMATH Keywords

integrabilitydiscrete dynamical systemsDarboux methodinvariant algebraic hypersurfaces

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Discrete version of topics in analysis (39A12) Invariant manifold theory for dynamical systems (37D10)

Related Items (14)

Liouvillian integrability versus Darboux polynomials ⋮ Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps ⋮ Invariants for certain discrete dynamical systems given by rational mappings ⋮ On invariants of discrete dynamical systems ⋮ Birational maps from polarization and the preservation of measure and integrals ⋮ A note on globally periodic maps and integrability ⋮ DYNAMICS OF SOME RATIONAL DISCRETE DYNAMICAL SYSTEMS VIA INVARIANTS ⋮ One class of planar rational involutions ⋮ A hybrid symbolic-numerical approach to the center-focus problem ⋮ Basis of absolute invariants of completely solvable linear and linear-fractional discrete dynamical systems ⋮ On invariants and invariant hypersurfaces of complex discrete dynamical systems ⋮ Global periodicity and complete integrability of discrete dynamical systems ⋮ Detecting and determining preserved measures and integrals of birational maps ⋮ Periodicity on discrete dynamical systems generated by a class of rational mappings

Cites Work

• On invariants for difference equations and systems of difference equations of rational form
• On the recursive sequence \(x_{n+1}=\alpha+x_{n-1}/x_n\)
• On rational recursive sequences
• Darboux integrability for 3D Lotka-Volterra systems
• Algorithms Involving Arithmetic and Geometric Means

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