TY - JOUR

T1 - Melnikov–Arnold integrals and optimal normal forms

AU - Шевченко, Иван Иванович

PY - 2026/4/1

Y1 - 2026/4/1

N2 - 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.

AB - 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.

UR - https://www.mendeley.com/catalogue/ff1e7b44-257c-38d6-b06a-fb82c462381a/

U2 - 10.1063/5.0307886

DO - 10.1063/5.0307886

M3 - Article

VL - 36

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 4

M1 - 043119

ER -