TY - JOUR

T1 - Lyapunov exponents in fundamental models of nonlinear resonance

AU - Шевченко, Иван Иванович

PY - 2024

Y1 - 2024

N2 - The problem of analytical estimation of the Lyapunov exponents and Lyapunov timescales of the motion in multiplets of interacting nonlinear resonances is considered. To this end, we elaborate a unified framework, based on the separatrix map theory, which incorporates both an earlier approach for the first fundamental model of perturbed resonance (given by the perturbed pendulum Hamiltonian) and a new one for its second fundamental model (given by the perturbed Andoyer Hamiltonian). Within this framework, new accurate estimates for the Lyapunov timescales of the inner and outer subsystems of the Solar planetary system are presented and discussed.

AB - The problem of analytical estimation of the Lyapunov exponents and Lyapunov timescales of the motion in multiplets of interacting nonlinear resonances is considered. To this end, we elaborate a unified framework, based on the separatrix map theory, which incorporates both an earlier approach for the first fundamental model of perturbed resonance (given by the perturbed pendulum Hamiltonian) and a new one for its second fundamental model (given by the perturbed Andoyer Hamiltonian). Within this framework, new accurate estimates for the Lyapunov timescales of the inner and outer subsystems of the Solar planetary system are presented and discussed.

UR - https://www.mendeley.com/catalogue/d9381768-ddd5-3090-b481-77bea971841e/

U2 - 10.1134/S0021364024602872

DO - 10.1134/S0021364024602872

M3 - Article

VL - 120

SP - 622

EP - 629

JO - JETP Letters

JF - JETP Letters

SN - 0021-3640

IS - 8

ER -