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Global attractor of a differentiable autonomous system on the plane

Nguyen Van Chau (1995)

Annales Polonici Mathematici

We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.

Hartman's theorem for complex flows in the Poincaré domain

John Guckenheimer (1972)

Compositio Mathematica

Hausdorff convergence and the limit shape of the unicorns.

Krauskopf, Bernd, Kriete, Hartje (1997)

Experimental Mathematics

Hyperbolicity, stability, and the criterion of homoclinic points.

Hayashi, Shuhei (1998)

Documenta Mathematica

Infinitely many coexisting strange attractors

Eduardo Colli (1998)

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

Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field

J. M. Gonçalves Ribeiro (1991)

Annales de l'I.H.P. Physique théorique

Invariant Sets of Anosovs Diffeomorphisms.

Ricardo Mané (1978)

Inventiones mathematicae

La dynamique au voisinage d'un point fixe elliptique conservatif : de Poincaré et Birkhoff à Aubry et Mather

Alain Chenciner (1983/1984)

Séminaire Bourbaki

Local structural stability of $C^{2}$ integrable 1-forms

Alcides Lins Neto (1977)

Annales de l'institut Fourier

In this work we consider a class of germs of singularities of integrable 1-forms in $R^{n}$ which are structurally stable in class $C^{r}$ ( $r \geq 2$ if $n = 3$ , $r \geq 4$ if $n \geq 4$ ), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.