POMULT: A program for computing periodic orbits in Hamiltonian systems based on multiple shooting algorithms

DOI10.1016/S0010-4655(97)00131-8zbMath0946.65129MaRDI QIDQ1299663

Stavros C. Farantos

Publication date: 10 October 2000

Published in: Computer Physics Communications (Search for Journal in Brave)

zbMATH Keywords

periodic orbitsequilibrium pointsfast Fourier transformLyapunov exponentsHamiltonian systemsPoincaré surfacesmultiple shooting algorithmdamped Newton-Raphson methodFortran 77 codePOMULT

Mathematics Subject Classification ID

Numerical methods for discrete and fast Fourier transforms (65T50) Periodic orbits of vector fields and flows (37C27) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (7)

Systematic search of symmetric periodic orbits in 2DOF Hamiltonian systems ⋮ Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori ⋮ Application of the characteristic bisection method for locating and computing periodic orbits in molecular systems ⋮ REACTION PATHS AND ELEMENTARY BIFURCATIONS TRACKS: THE DIABATIC ¹B₂-STATE OF OZONE ⋮ Systematic computer assisted proofs of periodic orbits of Hamiltonian systems ⋮ POMULT ⋮ Hamiltonian classical thermodynamics and chemical kinetics

Uses Software

• AUTO
• CANDYS/QA

Cites Work

• Asymptotic expansion and geometric properties of the spline collocation periodic solution of an ODE system
• On the numerical computation of Poincaré maps
• Bifurcations of periodic trajectories in non-integrable Hamiltonian systems with two degrees of freedom: Numerical and analytical results
• The calculation of periodic trajectories
• A stepsize control for continuation methods and its special application to multiple shooting techniques
• Two-sided approximation to periodic solutions of ordinary differential equations
• CANDYS/QA—A SOFTWARE SYSTEM FOR QUALITATIVE ANALYSIS OF NONLINEAR DYNAMICAL SYSTEMS
• Calculations of periodic trajectories for the Hénon–Heiles Hamiltonian using the monodromy method
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