From Poincaré maps to Lagrangian descriptors: the case of the valley ridge inflection point potential

DOI10.1134/S1560354721020040zbMath1490.37101arXiv2102.04904OpenAlexW3126860047MaRDI QIDQ2058465

Makrina Agaoglou, Rebecca Crossley, Matthaios Katsanikas, Stephen Wiggins

Publication date: 9 December 2021

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

Full work available at URL: https://arxiv.org/abs/2102.04904

zbMATH Keywords

heteroclinic orbithomoclinic orbitHamiltonian systeminvariant manifoldphase space structurePoincaré mapLagrangian descriptor

Mathematics Subject Classification ID

Hamilton's equations (70H05) Invariant manifolds for ordinary differential equations (34C45) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44) Numerical nonlinear stabilities in dynamical systems (65P40) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Computational methods for invariant manifolds of dynamical systems (37M21)

Related Items (5)

Phase Space Transport in a Symmetric Caldera Potential with Three Index-1 Saddles and No Minima ⋮ Geometric Parametrisation of Lagrangian Descriptors for 1 Degree-of-Freedom Systems ⋮ Visualizing the phase space of the HeI\(_2\) van der Waals complex using Lagrangian descriptors ⋮ Bifurcation study on a degenerate double van der Waals cirque potential energy surface using Lagrangian descriptors ⋮ Bifurcation of Dividing Surfaces Constructed from a Pitchfork Bifurcation of Periodic Orbits in a Symmetric Potential Energy Surface with a Post-Transition-State Bifurcation

Cites Work

• Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems
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• Lagrangian Descriptors for Stochastic Differential Equations: A Tool for Revealing the Phase Portrait of Stochastic Dynamical Systems
• A Theoretical Framework for Lagrangian Descriptors
• Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors
• Phase Space Analysis of the Nonexistence of Dynamical Matching in a Stretched Caldera Potential Energy Surface
• Phase Space Structure and Transport in a Caldera Potential Energy Surface
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Detection of Dynamical Matching in a Caldera Hamiltonian System Using Lagrangian Descriptors
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
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