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The global convergence of a direct method for determining turning (limit) points of a parameter-dependent mapping is analysed. It is assumed that the relevant extended system has a singular root for a special parameter value. The singular root is clasified as a $b i f u r c a t i o n s i n g u l a r i t y$ (i.e., as a $d e g e n e r a t e$ turning point). Then, the Theorz for Imperfect Bifurcation offers a particular scenario for the split of the singular root into a finite number of regular roots (turning points) due to a given parameter imperfection. The relationship...

A Hopf Bifurcation Theorem for Difference Equations Approximating a Differential Equation.

J. Hofbauer, G. Iooss (1984)

Monatshefte für Mathematik

A new chaotic attractor from 2D discrete mapping via border-collision period-doubling scenario.

Elhadj, Zeraoulia (2005)

Discrete Dynamics in Nature and Society

A new degree for $S^{1}$ -invariant gradient mappings and applications

E. N. Dancer (1985)

Annales de l'I.H.P. Analyse non linéaire

A new obstruction to embedding Lagrangian tori.

C. Viterbo (1990)

Inventiones mathematicae

A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.

Peter Smith (1990)

Revista Matemática de la Universidad Complutense de Madrid

Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle...

A study of the Rimmer bifurcation of symmetric fixed points of reversible diffeomorphisms.

Petrişor, Emilia (1996)

Balkan Journal of Geometry and its Applications (BJGA)

A sufficient condition for the existence of multiple periodic solutions of differential inclusions

Ralf Bader (1996)

Banach Center Publications

A Viterbo-Hofer-Zehnder type result for hamiltonian inclusions

Xianling Fan (1991)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Abelian integrals of quadratic Hamiltonian vector fields with an invariant straight line.

Chengzhi Li, Jaume Llibre, Zhi-fen Zhang (1995)

Publicacions Matemàtiques

We prove that the lowest upper bound for the number of isolated zeros of the Abelian integrals associated to quadratic Hamiltonian vector fields having a center and an invariant straight line after quadratic perturbations is one.

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4 Recherche d'orbites périodiques d'un champ hamiltonien associé à une structure symplectique non standard

A "Birkhoff-Lewis" type result for a class of Hamiltonian systems.

A construction of realizations of perturbations of Poincaré maps

A criterion for the non-existence of invariant circles

A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium

A geometric approach to a result of Benci and Giannoni for Hamiltonian systems with singular potentials.

A global analysis of Newton iterations for determining turning points