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Displaying similar documents to “Bifurcation of stationary and heteroclinic orbits for parametrized gradient-like flows”

Equivariant maps of joins of finite G-sets and an application to critical point theory

Danuta Rozpłoch-Nowakowska (1992)

Annales Polonici Mathematici

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A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function f : S n → ℝ , where G is a finite nontrivial group acting freely and orthogonally on ℝ n + 1 0 . Neither Morse theory nor the minimax method is applied. The proofs are based on a general version of Borsuk’s Antipodal Theorem for equivariant maps of joins of G-sets.

One-parameter families of brake orbits in dynamical systems

Lennard Bakker (1999)

Colloquium Mathematicae

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We give a clear and systematic exposition of one-parameter families of brake orbits in dynamical systems on product vector bundles (where the fiber has the same dimension as the base manifold). A generalized definition of a brake orbit is given, and the relationship between brake orbits and periodic orbits is discussed. The brake equation, which implicitly encodes information about the brake orbits of a dynamical system, is defined. Using the brake equation, a one-parameter family of...

Nonlinear eigenvalue problems for fourth order ordinary differential equations

Jolanta Przybycin (1995)

Annales Polonici Mathematici

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This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation...

Path formulation for multiparameter 𝔻 3 -equivariant bifurcation problems

Jacques-Élie Furter, Angela Maria Sitta (2010)

Annales de l’institut Fourier

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We implement a singularity theory approach, the path formulation, to classify 𝔻 3 -equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a 𝔻 3 -miniversal unfolding F 0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F 0 onto its unfolding parameter space. We apply our results...