On auto and hetero Bäcklund transformations for the Hénon-Heiles systems

DOI10.1016/j.physleta.2015.08.023zbMath1349.37072OpenAlexW2205193692MaRDI QIDQ341410

Andreĭ Vladimirovich Tsyganov

Publication date: 16 November 2016

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2015.08.023

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items

Reducible Abelian varieties and Lax matrices for Euler’s problem of two fixed centres, New bi-Hamiltonian systems on the plane, Reduction of divisors and the Clebsch system, On a family of Bäcklund transformations, Bäcklund transformations for the nonholonomic Veselova system, On exact discretization of cubic-quintic Duffing oscillator, Integrable discretization and deformation of the nonholonomic Chaplygin ball, Bäcklund transformations and divisor doubling, Ermakov-Pinney and Emden-Fowler equations: new solutions from novel Bäcklund transformations, Discretization and superintegrability all rolled into one, Reduction of divisors for classical superintegrable GL(3) magnetic chain, On discretization of the Euler top, Bäcklund transformations for the Jacobi system on an ellipsoid, Abel's theorem and Bäcklund transformations for the Hamilton-Jacobi equations, Discretization of Hamiltonian systems and intersection theory, Equivalent integrable metrics on the sphere with quartic invariants

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Hénon-Heiles system revisited
• On integrable Hamiltonians with velocity-dependent potentials
• Bäcklund transformations for finite-dimensional integrable systems: a geometric approach.
• On the Chaplygin system on the sphere with velocity dependent potential
• Simultaneous separation for the Neumann and Chaplygin systems
• Classical and quantum superintegrability with applications
• The analogue of the Backlund transformation for integrable many-body systems
• On Bäcklund transformations for many-body systems
• Bäcklund transformations and Hamiltonian flows
• Explicit integration of the Hénon-Heiles Hamiltonians 1