Work

Melnikov–Arnold integrals and optimal normal forms

Year: 2026

Type: article

Abstract: 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.

Source: Chaos An Interdisciplinary Journal of Nonlinear Science

DOI: 10.1063/5.0307886

Author: Ivan I. Shevchenko

Institutions: Russian Academy of Sciences, St Petersburg University, Institute of Applied Astronomy

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7154308055

FWCI:

Cites: 14

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