TY - GEN

T1 - Multibump trajectories of adiabatically perturbed periodic Hamiltonian systems with pitchfork bifurcations

AU - Ivanov, Alexey V.

AU - Panteleeva, Polina Yu.

PY - 2019

Y1 - 2019

N2 - We study a 1/2/-degrees of freedom Hamiltonian system with a potential U(x, εt) = 1/2(φ(εt)x 2 - x 4 ) slowly varying with time. It is assumed that the factor φ(τ) is a periodic function with simple zeroes on its period. Using WKB-method together with a modification of the Melnikov method, we prove that in the adiabatic limit a cascade of bifurcations, occuring when the factor φ passes through the zero value, leads to the existence of transversal homoclinic intersections and multibump trajectories of the system.

AB - We study a 1/2/-degrees of freedom Hamiltonian system with a potential U(x, εt) = 1/2(φ(εt)x 2 - x 4 ) slowly varying with time. It is assumed that the factor φ(τ) is a periodic function with simple zeroes on its period. Using WKB-method together with a modification of the Melnikov method, we prove that in the adiabatic limit a cascade of bifurcations, occuring when the factor φ passes through the zero value, leads to the existence of transversal homoclinic intersections and multibump trajectories of the system.

UR - https://ieeexplore.ieee.org/document/9016558/authors#authors

UR - https://ieeexplore.ieee.org/xpl/conhome/8999437/proceeding

UR - http://www.pdmi.ras.ru/~dd/download/PROC19.pdf

M3 - Conference contribution

SN - 978-1-7281-5837-2

SP - 78

EP - 83

BT - 2019 Days on Diffraction (DD)

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2019 International Conference on Days on Diffraction, DD 2019

Y2 - 3 June 2019 through 7 June 2019

ER -