 Effects of symmetry on instability-driven chaotic energy transport in near-integrable, Hamiltonian systemsM.Gregory Forest, Christopher G. Goedde and Amarendra Sinha Mathematics and Computers in Simulation (MATCOM), 1994, vol. 37, issue 4, 323-339 Abstract: Various remarkable nonlinear phenomena have been confirmed, discovered and explored through computer simulations of nearly integrable, Hamiltonian, large dimensional lattices with periodic boundary conditions. Here we pick the periodic sine-Gordon example of an “a priori unstable” integrable system which is then discretized spatially by an explicit non-integrable scheme. We then study the dynamics of this fixed, near-integrable Hamiltonian lattice and explore the transitions in short-time and long-time behavior as we initialize either far from or nearby integrable homoclinic structures. For this volume we specifically highlight the effects of symmetry. We illustrate a subtle phenomenon whereby small errors, on the order of machine arithmetic and roundoff error, may break a symmetry of the data and the equations, unleashing a symmetry-breaking instability absent in the symmetric subspace, and thereby exciting significant stochastic dynamics and energy transport nonexistent in the corresponding symmetric simulation. Date: 1994 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:37:y:1994:i:4:p:323-339 DOI: 10.1016/0378-4754(94)00022-0 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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