A family of integrable maps associated with the Volterra lattice

Relationships between algebraic curves and integrable systems (14H70) Rational and birational maps (14E05) Lattice dynamics; integrable lattice equations (37K60) Integrable difference and lattice equations; integrability tests (39A36) Completely integrable discrete dynamical systems (37J70)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Laurent phenomenon algebras
Discrete integrable systems and Poisson algebras from cluster maps
Integrable symplectic maps
Three-dimensional discrete systems of Hirota-Kimura type and deformed Lie-Poisson algebras
Hamiltonian structure of averaged difference systems
Completely integrable symplectic mapping
Three integrable Hamiltonian systems connected with isospectral deformations
On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices
On foundation of the generalized Nambu mechanics
A note on the averaging for single-phase elliptic solutions of the Toda and the Volterra lattices
Investigations on continued fractions
Algebraic entropy
Integrable mappings and soliton equations
Padé approximants on Riemann surfaces and KP tau functions
Asymptotic, algebraic and geometric aspects of integrable systems. In honor of Nalini Joshi on her 60th birthday. Selected papers of the workshop, TSIMF, Sanya, China, April 9--13, 2018
Singularity confinement for maps with the Laurent property
QRT maps and related Laurent systems
Discrete exact solutions of modified Volterra and Volterra lattice equations via the new discrete sine-Gordon expansion algorithm
Non-periodic continued fractions in hyperelliptic function fields
Dynamics of bimeromorphic maps of surfaces
Cluster algebras. I: Foundations
Investigation into the role of the Laurent property in integrability
On integrals for some class of ordinary difference equations admitting a Lax representation
On the Toda and KAC-VAN Moerbeke Systems
Discrete Painlevé II equation over finite fields
Analytic solutions and integrability for bilinear recurrences of order six
Note on the Poisson structure of the damped oscillator
ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON A SYSTEM OF CONTOURS, AND PERIODIC MOTIONS OF TODA LATTICES
A quadratic mapping with invariant cubic curve
Integrable maps
The discrete first, second and thirty-fourth Painlevé hierarchies
Integrable mappings of the plane preserving biquadratic invariant curves II
Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants
Some integrable maps and their Hirota bilinear forms
Hyperelliptic continued fractions and generalized Jacobians
Duality for discrete integrable systems
Continued Fractions and Hankel Determinants from Hyperelliptic Curves
On solutions for some class of integrable difference equations
Singularity confinement as an integrability criterion
Bi-rational maps in four dimensions with two invariants
Rational Maps with Invariant Surfaces
On the algebraic structure of rational discrete dynamical systems
Hankel Determinant Solutions to Several Discrete Integrable Systems and the Laurent Property
Sigma function solution of the initial value problem for Somos 5 sequences
Hyperelliptic curves, continued fractions, and Somos sequences
A novelnth order difference equation that may be integrable
On some classes of discrete polynomials and ordinary difference equations
A Riemann–Hilbert approach to the Akhiezer polynomials
On Stieltjes continued fractions.
Integrable systems in the realm of algebraic geometry.
On the autonomous limit of discrete Painlevé equations
Hermite-Padé approximation and integrability
Integrable maps in 4D and modified Volterra lattices