The effect of a singularity on transitions maps
Coll, Bartomeu (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)

Date:	2025
Abstract:	Consider a planar autonomous differential equation with a unique degenerated singularity inside a flow box with two transversal sections in such a way that a Poincar'e map between them is well defined by the flow. We are interested in understanding what effect this singularity has on the properties of the Poincar'e map between the transversal sections. The fiber containing the singularity is usually called singular fiber and, in particular, we want to determine its attractive or repulsive character. We prove that there is a real value whose sign determines the stability of the singular fiber. This value is given by the principal value of a suitable integral constructed from the corresponding differential equation.
Grants:	Agencia Estatal de Investigación PID2023-151974NB-I00 Agencia Estatal de Investigación PID2022-136613NB-I00 Generalitat de Catalunya 2021/SGR-00113
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Degenerate singularities ; Transition map ; Stability
Published in:	Discrete and continuous dynamical systems. Series S, Vol. 18, Num. 12 (December 2025) , p. 4021-4039, ISSN 1937-1179

DOI: 10.3934/dcdss.2025125

Postprint 19 p, 408.8 KB

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