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The paper contains a generic condition permitting the linearization in class $𝒞^{k}$ , $0 \leq k \leq \infty$ , of germs of singular infinitesimal $R^{2}$ -actions on $R^{n}$ $(n \geq 2)$ and of singular holomorphic...

Smooth normalization of a vector field near a semistable limit cycle

Sergey Yu. Yakovenko (1993)

Annales de l'institut Fourier

We establish a polynomial normal form for a vector field having a limit cycle of multiplicity 2. The smooth classification problem for such fields is closely related to the problem of classification of germs $Δ : (ℝ^{1}, 0) \to (ℝ^{1}, 0)$ , $Δ (x) = x + c x^{2} + \dots$ , solved by F. Takens in 1973. Such germs appear as the germs of Poincaré return maps for semistable cycles, and a smooth conjugacy between any two such germs may be extended to a smooth orbital equivalence between the original fields.If one deals with smooth conjugacy of flows rather than...

Smooth transformations of intervals

Oscar E. Lanford III (1980/1981)

Séminaire Bourbaki

Smoothness property for bifurcation diagrams.

Robert Roussarie (1997)

Publicacions Matemàtiques

Strata of bifurcation sets related to the nature of the singular points or to connections between hyperbolic saddles in smooth families of planar vector fields, are smoothly equivalent to subanalytic sets. But it is no longer true when the bifurcation is related to transition near singular points, for instance for a line of double limit cycles in a generic 2-parameter family at its end point which is a codimension 2 saddle connection bifurcation point. This line has a flat contact with the line...

Solutions périodiques de systèmes hamiltoniens

Henri Berestycki (1982/1983)

Séminaire Bourbaki

Solutions with minimal period for hamiltonian systems in a potential well

Antonio Ambrosetti, Vittorio Coti Zelati (1987)

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

Some perturbation results for non-linear problems

Carlo Carminati (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.

Spectrum of the Poincaré Map for Periodic Reflecting Rays in Generic Domains.

Luchezar Stojanov, Vesselin Petkov (1987)

Mathematische Zeitschrift

Stability of fixed points for order-preserving discrete-time dynamical systems.

E.N. Dancer, P. Hess (1991)

Journal für die reine und angewandte Mathematik

Stable intersections of Cantor sets and homoclinic bifurcations

Carlos Gustavo T. de A. Moreira (1996)

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

Stochastic behavior above Feigenbaum's parameter value

M. V. Jakobson, A. M. Stepin (1989)

Banach Center Publications

Subharmonics of convex non-coercive Hamiltonian systems.

Mohsen Timoumi (1992)

Collectanea Mathematica

Sur l'équation aux différences affine du premier ordre unidimensionnelle

Augustin Fruchard (1996)

Annales de l'institut Fourier

On étudie les phénomènes de retard à la bifurcation et de butée pour des systèmes discrets lents-rapides du plan. On donne une explication géométrique de ces phénomènes basée sur l’examen de fonctions reliefs. On démontre ensuite l’existence et la vie brève des longs canards, qui sont des trajectoires ne présentant pas de butée. Trois exemples illustrent ces phénomènes. Le premier expose la problématique, le second permet une expérimentation de l’étude théorique sur les longs canards, le troisième...

Symbolic dynamics and geodesic flows

Mark Pollicott (1991/1992)

Séminaire de théorie spectrale et géométrie

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