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Homoclinic transversal trajectories of singularly perturbed periodic Hamiltonian systems with disappearing separatrix. / Ivanov, Alexey V.; Panteleeva, Polina Yu.

Proceedings of the International Conference Days on Diffraction 2021, DD 2021. 2021. стр. 87-92.

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Harvard

Ivanov, AV & Panteleeva, PY 2021, Homoclinic transversal trajectories of singularly perturbed periodic Hamiltonian systems with disappearing separatrix. в Proceedings of the International Conference Days on Diffraction 2021, DD 2021. стр. 87-92, Days on Diffraction 2021, St. Petersburg, Российская Федерация, 31/05/21. https://doi.org/10.1109/DD52349.2021.9598745

APA

Ivanov, A. V., & Panteleeva, P. Y. (2021). Homoclinic transversal trajectories of singularly perturbed periodic Hamiltonian systems with disappearing separatrix. в Proceedings of the International Conference Days on Diffraction 2021, DD 2021 (стр. 87-92) https://doi.org/10.1109/DD52349.2021.9598745

Vancouver

Ivanov AV, Panteleeva PY. Homoclinic transversal trajectories of singularly perturbed periodic Hamiltonian systems with disappearing separatrix. в Proceedings of the International Conference Days on Diffraction 2021, DD 2021. 2021. стр. 87-92 https://doi.org/10.1109/DD52349.2021.9598745

Author

Ivanov, Alexey V. ; Panteleeva, Polina Yu. / Homoclinic transversal trajectories of singularly perturbed periodic Hamiltonian systems with disappearing separatrix. Proceedings of the International Conference Days on Diffraction 2021, DD 2021. 2021. стр. 87-92

BibTeX

@inproceedings{fb922da21b184f3c8f243f41e506258d,
title = "Homoclinic transversal trajectories of singularly perturbed periodic Hamiltonian systems with disappearing separatrix",
abstract = "We study a Hamiltonian system with 1.5 degrees of freedom with a Hamiltonian slowly varying in time. The bifurcation parameter of the system is a twice continuously differentiable periodic function with simple zeros. The presence of zeros of the function implies existence of a cascade of pitchfork bifurcations in the phase space of the {"}frozen{"}system. In this work we obtain a sufficient condition for the existence of transversal {"}rotating{"}homoclinic trajectories of the system. The result is based on asymptotic analysis of solutions to the Cauchy problem in different domains of the phase space.",
author = "Ivanov, {Alexey V.} and Panteleeva, {Polina Yu}",
year = "2021",
month = jan,
day = "1",
doi = "10.1109/DD52349.2021.9598745",
language = "English",
pages = "87--92",
booktitle = "Proceedings of the International Conference Days on Diffraction 2021, DD 2021",
note = "2021 International Conference Days on Diffraction, DD 2021 ; Conference date: 31-05-2021 Through 04-06-2021",
url = "http://www.pdmi.ras.ru/~dd/",

}

RIS

TY - GEN

T1 - Homoclinic transversal trajectories of singularly perturbed periodic Hamiltonian systems with disappearing separatrix

AU - Ivanov, Alexey V.

AU - Panteleeva, Polina Yu

PY - 2021/1/1

Y1 - 2021/1/1

N2 - We study a Hamiltonian system with 1.5 degrees of freedom with a Hamiltonian slowly varying in time. The bifurcation parameter of the system is a twice continuously differentiable periodic function with simple zeros. The presence of zeros of the function implies existence of a cascade of pitchfork bifurcations in the phase space of the "frozen"system. In this work we obtain a sufficient condition for the existence of transversal "rotating"homoclinic trajectories of the system. The result is based on asymptotic analysis of solutions to the Cauchy problem in different domains of the phase space.

AB - We study a Hamiltonian system with 1.5 degrees of freedom with a Hamiltonian slowly varying in time. The bifurcation parameter of the system is a twice continuously differentiable periodic function with simple zeros. The presence of zeros of the function implies existence of a cascade of pitchfork bifurcations in the phase space of the "frozen"system. In this work we obtain a sufficient condition for the existence of transversal "rotating"homoclinic trajectories of the system. The result is based on asymptotic analysis of solutions to the Cauchy problem in different domains of the phase space.

UR - http://www.scopus.com/inward/record.url?scp=85123291258&partnerID=8YFLogxK

U2 - 10.1109/DD52349.2021.9598745

DO - 10.1109/DD52349.2021.9598745

M3 - Conference contribution

AN - SCOPUS:85123291258

SP - 87

EP - 92

BT - Proceedings of the International Conference Days on Diffraction 2021, DD 2021

T2 - 2021 International Conference Days on Diffraction, DD 2021

Y2 - 31 May 2021 through 4 June 2021

ER -

ID: 95584575