The phase portrait of the Hamiltonian system associated to a Pinchuk map

The phase portrait of the Hamiltonian system associated to a Pinchuk map

In this paper we describe the global phase portrait of the Hamiltonian system associated to a Pinchuk map in the Poincaré disc. In particular, we prove that this phase portrait has 15 separatrices, five of them singular points, and 7 canonical regions, six of them of type strip and one annular.

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Veröffentlicht in:Anais da Academia Brasileira de Ciências 2018-07, Vol.90 (3), p.2599-2616
Hauptverfasser: Artés, Joan Carles, Braun, Francisco, Llibre, Jaume
Format: Artikel
Sprache:eng
Schlagworte:
center
global injectivity
MULTIDISCIPLINARY SCIENCES
Pinchuk map
real Jacobian conjecture
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Zusammenfassung:In this paper we describe the global phase portrait of the Hamiltonian system associated to a Pinchuk map in the Poincaré disc. In particular, we prove that this phase portrait has 15 separatrices, five of them singular points, and 7 canonical regions, six of them of type strip and one annular.
ISSN:0001-3765
1678-2690
1678-2690
DOI:10.1590/0001-3765201820170829