Affine Weyl groups, discrete dynamical systems and Painleve equations

Abstract

A new class of representations of affine Weyl groups on rational functions are constructed, in order to formulate discrete dynamical systems associated with affine root systems. As an application, some examples of difference and differential systems of Painleve type are discussed.

AMSLaTeX, 16 pages

Cited by in corpus (41)

• Yang-Baxter maps and integrable dynamics
• Geometric Aspects of Painlevé Equations
• A study on the fourth q-Painlevé equation
• Diophantine Integrability
• Painleve equations from Darboux chains - Part 1: P3-P5
• The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
• Elliptic Calogero-Moser Systems and Isomonodromic Deformations
• Invariants in Separated Variables: Yang-Baxter, Entwining and Transfer Maps
• Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations
• Deformation of Okamoto-Painlevé Pairs and Painlevé equations
• On the Linearization of the First and Second Painleve' Equations
• The Coxeter relations and KP map for non-commuting symbols
• Elliptic (N,N^\prime)-Soliton Solutions of the lattice KP Equation
• Factorization of Combinatorial R matrices and Associated Cellular Automata
• Rational solutions of the Noumi and Yamada system of type $A_4^{(1)}$
• Rational Solutions of the Fifth Painlevé Equation. Generalised Laguerre Polynomials
• W(E_10) Symmetry, M-Theory and Painleve Equations
• On Some Applications of Sakai's Geometric Theory of Discrete Painlevé Equations
• Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
• A Symmetric System of Mixed Painleve III - V Equations and its Integrable Origin
• Unitary matrix with a Penner-like potential also yields N_f=2
• Similarity reduction of the modified Yajima-Oikawa equation
• T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras
• Two-component Yang-Baxter maps and star-triangle relations
• Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings
• Gauge Symmetry Origin of Bäcklund Transformations for Painlevé Equations
• From Polygons to Ultradiscrete Painlevé Equations
• Geometric description of discrete power function associated with the sixth Painlevé equation
• Airy series solution of Painlevé II in electrodiffusion: conjectured convergence
• A Dynamical Systems Approach to The Fourth Painleve Equation
• On Rational Solutions of Dressing Chains of Even Periodicity
• Quantizing the discrete Painlevé VI equation : The Lax formalism
• A symmetry reduction technique for higher order Painlevé systems
• Reduction of lattice equations to the Painlevé equations: P${}_{\mathrm{IV}}$ and P${}_{\mathrm{V}}$
• Coalescence, Deformation and Bäcklund Symmetries of Painlevé IV and II Equations
• On Hamiltonian Formalism for Dressing Chain Equations of Even Periodicity
• Bäcklund transformations as integrable discretization. The geometric approach
• Symmetries in Connection Preserving Deformations
• Extended symmetry of higher Painlevé equations of even periodicity and their rational solutions
• Discrete equations from Bäcklund transformations of the fifth Painlevé equation
• Differential equations for the closed geometric crystal chains