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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2003, Volume 9, Number 1, Pages 159–164 (Mi timm269)  
On the dynamic unfolding of a saddle-center bifurcation and the change in the action

R. Habermana, D. C. Diminnieb

a Department of Mathematics, Southern Methodist University, Dallas, USA
b Texas Instruments Incorporated, Dallas, USA
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Abstract: Conservative Hamiltonian systems with slow variations are considered in the case of a dynamic saddle-center bifurcation. Using the method of averaging, action is an adiabatic invariant before and after the slow passage of the homoclinic orbit. The bifurcation is unfolded by assuming that the time that the method of averaging predicts that the homoclinic orbit is crossed is near to the time of the saddle-center bifurcation. The slow passage through homoclinic orbits associated with the unfolding of a saddle-center bifurcation is analyzed and the change in the adiabatic invariant is computed.
Received: 11.11.2002
Bibliographic databases:
Document Type: Article
UDC: 519.632
Language: English
Citation: R. Haberman, D. C. Diminnie, “On the dynamic unfolding of a saddle-center bifurcation and the change in the action”, Asymptotic expansions, approximation theory, topology, Trudy Inst. Mat. i Mekh. UrO RAN, 9, no. 1, 2003, 159–164; Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S91–S97
Citation in format AMSBIB
\Bibitem{HabDim03}
\by R.~Haberman, D.~C.~Diminnie
\paper On the dynamic unfolding of a~saddle-center bifurcation and the change in the action
\inbook Asymptotic expansions, approximation theory, topology
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2003
\vol 9
\issue 1
\pages 159--164
\mathnet{http://mi.mathnet.ru/timm269}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2093434}
\zmath{https://zbmath.org/?q=an:1123.37315}
\elib{https://elibrary.ru/item.asp?id=12226589}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2003
\issue , suppl. 1
\pages S91--S97
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