Work

On the critical points of planar polynomial Hamiltonian systems

Year: 2025

Type: article

Abstract: It is well known that the critical points of planar polynomial Hamiltonian vector fields are either centers or points with an even number of hyperbolic sectors. We give a sharp upper bound of the number of centers that these systems can have in terms of the degrees of their components. We also prove that generically the critical points at infinity of their Poincaré compactification are either nodes or have indices − 1 , 0 or 1 and have at most two sectors: both hyperbolic, both elliptic or one of each type. These characteristics are no more true in the non generic situation. Although these results are known we revisit their proofs. The new proofs are shorter and based on a new approach.

Source: Nonlinear Analysis Real World Applications

DOI: 10.1016/j.nonrwa.2025.104503

Authors: Anna Cima, Armengol Gasull, Francesc Mañosas

Institution: Universitat Autònoma de Barcelona

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funders: Ministerio de Ciencia, Innovación y Universidades, Generalitat de Catalunya, Ministerio de Ciencia e Innovación, Agència de Gestió d'Ajuts Universitaris i de Recerca