Numerical Continuation of Hamiltonian Relative Periodic Orbits

Keywords

Numerical continuation, Hamiltonian system, Mathematics, Bifurcation, Continuation

References

• Persistance d?orbites priodiques relatives dans les systmes hamiltoniens symtriquesJames Montaldi — 1997
• Newton Methods for Nonlinear ProblemsPeter Deuflhard — 2004
• Infinite bifurcations in the restricted three-body problemG. Contopoulos, A. D. Pinotsis — 1984
• Numerical Continuation of Periodic Orbits with Symmetry.Claudia Wulff, Andreas Hohmann, Peter Deuflhard — 1994
• Scientific Computing with Ordinary Differential EquationsDeuflhard, Peter 1944-2019, Bornemann, Folkmar 1967- — 2002
• Global Bifurcation of Periodic Solutions with SymmetryBernold Fiedler — 1988
• Singularities and groups in bifurcation theoryMartin Golubitsky, Ian Stewart, David G. Schaeffer — 1985
• Stability and bifurcations of the figure-8 solution of the three-body problem.J. Galán, Francisco Javier Muñoz–Almaraz, E. Freire — 2002
• Bifurcation from relative periodic solutionsClaudia Wulff, Jeroen S.W. Lamb, Ian Melbourne — 2001
• Reversible Relative Periodic OrbitsJeroen S.W. Lamb, Claudia Wulff — 2002
• Efficient numerical path following beyond critical pointsPeter Deuflhard, Bernold Fiedler, Peter Kunkel — 1987
• Numerical Continuation of Symmetric Periodic OrbitsClaudia Wulff, Andreas Schebesch — 2006
• Persistence of Hamiltonian relative periodic orbitsClaudia Wulff — 2003
• Symbolic exploitation of symmetry in numerical pathfollowingKarin Gatermann, Andreas Hohmann — 1991
• Families of periodic orbits in the planar three-body problemJohn D. Hadjidemetriou, Th. Christides — 1975
• Bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactionsJeroen S. W. Lamb, Ian Melbourne, Claudia Wulff — 2003
• Computation of periodic solutions of nonlinear odesPeter Deuflhard — 1984
• Families of periodic orbits in the three-body problemM. Hénon — 1974
• Hamiltonian Systems Near Relative Periodic OrbitsClaudia Wulff, Mark Roberts — 2002
• Bifurcation from Discrete Rotating WavesJeroen S.W. Lamb, Ian Melbourne — 1999

Cited by

• Metody numeryczne rozwiązywania, analizy i kontroli nieciągłych układów dynamicznychPaweł Olejnik — 2013
• Continuation of periodic orbits in symmetric Hamiltonian and conservative systemsJ. Galán, Francisco Javier Muñoz Almaraz, E. Freire — 2014
• Numerical Bifurcation of Hamiltonian Relative Periodic OrbitsClaudia Wulff, Frank Schilder — 2009
• Numerical Continuation of Symmetric Periodic OrbitsClaudia Wulff, Andreas Schebesch — 2006
• Relative Lyapunov Center BifurcationsClaudia Wulff, Frank Schilder — 2014
• Periodic solutions of the N-body problem with Lennard-Jones-type potentialsLuca Sbano, John. Southall — 2010
• Energy-conserving methods for Hamiltonian boundary value problems and applications in astrodynamicsPierluigi Amodio, Luigi Brugnano, Felice Iavernaro — 2013
• Advanced Topics in Numerical and Computational Bifurcation Analysis: Assignment ProjectsEusebius J. Doedel, Claudia Wulff, Harry Dankowicz — 2011
• An Approximation Method for the Numerical Solution of Planar Discontinuous Dynamical Systems with Stick-Slip FrictionPaweł Olejnik, Jan Awrejcewicz, Mičhal Fĕckan — 2014
• From the Lagrange polygon to the figure eight IRenato Calleja, Carlos García-Azpeitia, Jean‐Philippe Lessard — 2020
• Numerical approach for bifurcation and orbital stability analysis of periodic motions of a 2-DOF autonomous Hamiltonian systemEgor Sukhov — 2021
• Continuation of Periodic Orbits in Symmetric Hamiltonian SystemsJ. Galán-Vioque, A. Vanderbauwhede — 2007

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