A Methodology for the Numerical Computation of Normal Forms, Centre Manifolds and First Integrals of Hamiltonian Systems
DOI10.1080/10586458.1999.10504397zbMath0983.37107OpenAlexW2036685798MaRDI QIDQ4523665
Publication date: 14 January 2001
Published in: Experimental Mathematics (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/232007
Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcations and instability for nonlinear problems in mechanics (70K50) Hamilton's equations (70H05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Celestial mechanics (70F15) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical problems in dynamical systems (65P99) Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory (37-04) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A dynamical equivalent to the equilateral libration points of the Earth- Moon system
- On the stability of the Lagrangian points in the spatial restricted problem of three bodies
- The stability of the Lagrange triangular point and a theorem of Arnold
- Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
- Perturbation methods, bifurcation theory and computer algebra
- Construction of analytic KAM-surfaces and effective stability bounds
- Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
- Study of the transfer from the Earth to a halo orbit around the equilibrium point \(L_ 1\)
- On the persistence of lower dimensional invariant tori under quasi-periodic perturbations
- Dynamics in the center manifold of the collinear points of the restricted three-body problem
- Numerical computation of normal forms around some periodic orbits of the restricted three-body problem
- A general precompiler for algebraic manipulation
- A FORTRAN-based Poisson series processor and its applications in celestial mechanics
- On the normal behaviour of partially elliptic lower-dimensional tori of Hamiltonian systems
- The quasi integrals
- A note on a Lagrangian formulation for motion about the collinear points
- Accurate strategies for small divisor problems
- ON MOULTON'S ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES
- Introduction to Hamiltonian dynamical systems and the \(N\)-body problem