Transition state theory with quasi-periodic forcing

DOI10.1016/j.cnsns.2018.02.014zbMath1470.37045OpenAlexW2792659699MaRDI QIDQ2207898

Lei Zhang, Rafael de la Llave

Publication date: 23 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2018.02.014

zbMATH Keywords

normally hyperbolic invariant manifoldsquasi-periodic systemstransition state theory

Mathematics Subject Classification ID

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Chemical kinetics in thermodynamics and heat transfer (80A30) Invariant manifold theory for dynamical systems (37D10)

Related Items (6)

High-order resonant orbit manifold expansions for mission design in the planar circular restricted 3-body problem ⋮ Numerical Computation of High-Order Expansions of Invariant Manifolds of High-Dimensional Tori ⋮ Resonant tori, transport barriers, and chaos in a vector field with a Neimark-Sacker bifurcation ⋮ Time dependent center manifold in PDEs ⋮ Rapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problems ⋮ Asymmetric propagation of acoustic waves in a conical granular chain

Uses Software

• FFTW
• GSL

Cites Work

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• The parameterization method for invariant manifolds. From rigorous results to effective computations
• A note on the fractalization of saddle invariant curves in quasiperiodic systems
• Parameterization of slow-stable manifolds and their invariant vector bundles: theory and numerical implementation
• Triple collisions of invariant bundles
• Fast iteration of cocycles over rotations and computation of hyperbolic bundles
• Geometric proof for normally hyperbolic invariant manifolds
• Cone conditions and covering relations for topologically normally hyperbolic invariant manifolds
• Propagation of large uncertainty sets in orbital dynamics by automatic domain splitting
• Tools to detect structures in dynamical systems using jet transport
• Persistance et bifurcation de tores invariants
• A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results
• A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms
• Computation of maximal local (un)stable manifold patches by the parameterization method
• Approximately invariant manifolds and global dynamics of spike states
• Covering relations and the existence of topologically normally hyperbolic invariant sets
• Dédoublement de courbes invariantes sur le cylindre: petits diviseurs. (Small divisors phenomena in an invariant curve doubling bifurcation on a cylinder)
• Quasi-genericity of bifurcations to high dimensional invariant tori for maps
• Bifurcation of higher dimensional Tori
• Invariant manifolds associated to nonresonant spectral subspaces
• Algorithms for computing normally hyperbolic invariant manifolds
• Computation of quasi-periodic normally hyperbolic invariant tori: algorithms, numerical explorations and mechanisms of breakdown
• Invariant manifolds and the parameterization method in coupled energy harvesting piezoelectric oscillators
• The parameterization method for invariant manifolds. III: Overview and applications
• Computer assisted proof for normally hyperbolic invariant manifolds
• Reliable Computation of Robust Response Tori on the Verge of Breakdown
• Collision of invariant bundles of quasi-periodic attractors in the dissipative standard map
• The geometry of reaction dynamics
• Breakdown mechanisms of normally hyperbolic invariant manifolds in terms of unstable periodic orbits and homoclinic/heteroclinic orbits in Hamiltonian systems
• Manifolds on the verge of a hyperbolicity breakdown
• Nonnormally hyperbolic invariant curves for maps in R³and doubling bifurcation
• Chaotic transport in the homoclinic and heteroclinic tangle regions of quasiperiodically forced two-dimensional dynamical systems
• Note on sums containing small divisors
• Persistent manifolds are normally hyperbolic
• The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
• The parameterization method for invariant manifolds II: regularity with respect to parameters
• Different scenarios for hyperbolicity breakdown in quasiperiodic area preserving twist maps
• A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi‐Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity
• Bifurcations of transition states: Morse bifurcations
• Wigner's dynamical transition state theory in phase space: classical and quantum
• Universal asymptotics in hyperbolicity breakdown

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