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Main Author: Shevchenko, Ivan I.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.13840
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author Shevchenko, Ivan I.
author_facet Shevchenko, Ivan I.
contents The Melnikov-Arnold integrals (MA-integrals) is a well-known instrument used to measure the splitting of separatrices in Hamiltonian systems. In this article, we explore how calculation of MA-integrals can be used as well to estimate sizes of secondary resonances. Within the standard map model, we show how the newly developed MA-based procedure allows one to estimate the sizes of secondary resonances of any order (up to the order of the optimal normal form), without relying on the cumbersome traditional normalization procedure.
format Preprint
id arxiv_https___arxiv_org_abs_2604_13840
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Melnikov-Arnold integrals and optimal normal forms
Shevchenko, Ivan I.
Chaotic Dynamics
The Melnikov-Arnold integrals (MA-integrals) is a well-known instrument used to measure the splitting of separatrices in Hamiltonian systems. In this article, we explore how calculation of MA-integrals can be used as well to estimate sizes of secondary resonances. Within the standard map model, we show how the newly developed MA-based procedure allows one to estimate the sizes of secondary resonances of any order (up to the order of the optimal normal form), without relying on the cumbersome traditional normalization procedure.
title Melnikov-Arnold integrals and optimal normal forms
topic Chaotic Dynamics
url https://arxiv.org/abs/2604.13840