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arXiv · 2610.33620

Zeros of Melnikov functions for periodically perturbed Hamiltonian systems with random coefficients

Ali Ittayem·Erik Lundberg
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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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Ali Ittayem, Erik Lundberg. 2026-10-24. Zeros of Melnikov functions for periodically perturbed Hamiltonian systems with random coefficients. https://arxiv.org/abs/2610.33620

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