PreprintarXiv licencearXiv
Zeros of Melnikov functions for periodically perturbed Hamiltonian systems with random coefficients
Abstract
Introducing a probabilistic perspective on a classical theme within the study of chaotic dynamics, we investigate the zeros of the Melnikov distance function associated to a periodically perturbed Hamiltonian system when the perturbation has random coefficients. We provide asymptotic estimates (as the period of the perturbation becomes large or small) for the average number of zeros and for the probability of no zeros.
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BibTeX
@misc{ittayem2026zeros,
title = {{Zeros of Melnikov functions for periodically perturbed Hamiltonian systems with random coefficients}},
author = {Ali Ittayem and Erik Lundberg},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33620},
eprint = {2610.33620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33620},
}
RIS
TY - UNPB
TI - Zeros of Melnikov functions for periodically perturbed Hamiltonian systems with random coefficients
AU - Ali Ittayem
AU - Erik Lundberg
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33620
UR - https://arxiv.org/abs/2610.33620
AB - Introducing a probabilistic perspective on a classical theme within the study of chaotic dynamics, we investigate the zeros of the Melnikov distance function associated to a periodically perturbed Hamiltonian system when the perturbation has random coefficients. We provide asymptotic estimates (as the period of the perturbation becomes large or small) for the average number of zeros and for the probability of no zeros.
ER -