Quasi-Invariant Manifolds, Stability, and Generalized Hopf Bifurcation

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Quasi-Invariant Manifolds, Stability, and Generalized Hopf Bifurcation

Show simple item record Salvadori, L. en Bernfeld, Stephen R. en 2010-06-09T15:14:23Z en 2010-06-09T15:14:23Z en 1981-03 en
dc.identifier.uri en
dc.description.abstract We are interested in obtaining an analysis of the bifurcating periodic orbits arising in the generalized Hopf bifurcation problems in Rn. The existence of these periodic orbits has often been obtained by using such techniques as the Lyapunov-Schmidt method or topological degree arguments (see Marsden and McCracken [8] and Hale [6] and their references). Our approach, on the other bend, is based upon stability properties of the equilibrium point of the unperturbed system. Andronov et. al. [1] showed the fruitfulness of this approach in studying bifurcation problems in R2 (for more recent papers see Negrini and Salvadori [9] and Bernfeld and Salvadori [2]). In the case of R2, in contrast to that of Rn, n > 2, the stability arguments can be effectively applied because of the Poincaré-Bendixson theory. Bifurcation problems in Rn can be reduced to that of R2 when two dimensional invariant manifolds are known to exist. The existence of such manifolds occurs, or example when the unperturbed system contains only two purely imaginary eigenvalues. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;153 en
dc.subject Bifurcating periodic orbits en
dc.subject Hopf bifurcation en
dc.subject Topological degree arguments en
dc.subject Stability properties en
dc.subject Poincaré-Bendixson theory en
dc.subject Imaginary eigenvalues en
dc.subject Mathematics Research en
dc.title Quasi-Invariant Manifolds, Stability, and Generalized Hopf Bifurcation en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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