Bäcklund transformations for the nonholonomic Veselova system

DOI10.1134/S1560354717020058zbMath1375.37157arXiv1703.04251MaRDI QIDQ2400445

Andreĭ Vladimirovich Tsyganov

Publication date: 1 September 2017

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.04251

zbMATH Keywords

Bäcklund transformationbi-Hamiltonian geometrynonholonomic dynamical system

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Nonholonomic dynamical systems (37J60)

Related Items (11)

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Cites Work

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• Hamiltonization of elementary nonholonomic systems
• On auto and hetero Bäcklund transformations for the Hénon-Heiles systems
• The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere
• On a class of integrable systems with a quartic first integral
• One family of conformally Hamiltonian systems
• Bäcklund transformations relating different Hamilton-Jacobi equations
• Abel's theorem and Bäcklund transformations for the Hamilton-Jacobi equations
• Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems
• Reduction of almost Poisson brackets for nonholonomic systems on Lie groups
• Killing tensors with nonvanishing Haantjes torsion and integrable systems
• Discrete nonholonomic Lagrangian systems on Lie groupoids
• Bäcklund transformations and divisor doubling
• On the Poisson structures for the nonholonomic Chaplygin and Veselova problems
• Nonholonomic LR systems as generalized Chaplygin systems with an invariant measure and flows on homogeneous spaces
• Formulae for arithmetic on genus 2 hyperelliptic curves
• Bäcklund transformations for finite-dimensional integrable systems: a geometric approach.
• Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds
• On the Chaplygin system on the sphere with velocity dependent potential
• Simultaneous separation for the Neumann and Chaplygin systems
• A Canonical Transformation for the Exponential Lattice
• Group Law Computations on Jacobians of Hyperelliptic Curves
• Non-holonomic dynamics and Poisson geometry
• The analogue of the Backlund transformation for integrable many-body systems
• Computing in the Jacobian of a Hyperelliptic Curve
• Generalizations of classical integrable nonholonomic rigid body systems
• The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body
• On the Routh sphere problem
• A new integrable problem with a quartic integral in the dynamics of a rigid body
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• Two-dimensional geodesic flows having first integrals of higher degree

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