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Updated: Jan 26, 2026
Three-Dimensional Reconstruction of Orbital Fractures
Published on: May 16, 2025
Effect of colored noise on heteroclinic orbits
1Université de Caen Normandie, ESIX Cherbourg, ABTE EA4651-ToxEMAC, 14000 Caen, France.
Abstract:
The dynamics of a weakly dissipative Hamiltonian system submitted to stochastic perturbations has been investigated by means of asymptotic methods. The probability of noise-induced separatrix crossing, which drastically changes the fate of the system, is derived analytically in the case where noise is an additive Kubo-Anderson process. This theory shows how the geometry of the separatrix, as well as the noise intensity and correlation time, affect the statistics of crossing. Results can be applied to a wide variety of systems, and are valid in the limit where the noise correlation time scale is much smaller than the time scale of the undisturbed Hamiltonian dynamics.
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