A study of the Rimmer bifurcation of symmetric fixed points of reversible diffeomorphisms.
Petrişor, Emilia (1996)
Balkan Journal of Geometry and its Applications (BJGA)
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Petrişor, Emilia (1996)
Balkan Journal of Geometry and its Applications (BJGA)
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Dzedzej, Zdzisław (2003)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Kuehn, Christian (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Ward, James R. jun. (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Fassó, Francesco, Giacobbe, Andrea (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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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 , where G is a finite nontrivial group acting freely and orthogonally on . 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.
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...
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...
Dragana Ranković (2011)
Matematički Vesnik
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Shapakidze, L. (1997)
Georgian Mathematical Journal
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Stewart, Ian (2003)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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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 -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 -miniversal unfolding of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of onto its unfolding parameter space. We apply our results...