Bifurcations of periodic solutions of a Hamiltonian system with a discrete symmetry group

DOI10.1134/S0361768820020036zbMath1459.37042OpenAlexW3016596299MaRDI QIDQ2217194

A. B. Batkhin

Publication date: 18 December 2020

Published in: Programming and Computer Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0361768820020036

zbMATH Keywords

Gröbner basesmonodromy matrixKlein four-groupsymplectic transformations

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Numerical bifurcation problems (65P30) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Symplectic and canonical mappings (37J11) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Related Items (2)

Five new methods of celestial mechanics ⋮ Symbolic methods for studying the equilibrium orientations of a system of two connected bodies in a circular orbit

Uses Software

• Maple
• Mathematica
• SymPy
• TIDES
• Taylor

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Systematic search of symmetric periodic orbits in 2DOF Hamiltonian systems
• Families of asymmetric periodic orbits in Hill's problem of three bodies
• Time-reversal symmetry in dynamical systems: a survey
• New families of periodic orbits in Hill's problem of three bodies
• Web of families of periodic orbits of the generalized Hill problem
• Algorithm 924
• A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods
• ON MOULTON'S ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES
• Algebraic proof of the non-integrability of Hill's problem
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem
• Periodic solutions of the N-body problem

This page was built for publication: Bifurcations of periodic solutions of a Hamiltonian system with a discrete symmetry group