Derivatives of the Separation Function of Generalized Saddle Connections
Marín Pérez, David (Universitat Autònoma de Barcelona)
Villadelprat Yagüe, Jordi (Universitat Autònoma de Barcelona)

Data:	2025
Resum:	A classical formula shows that the breaking of a connection between two hyperbolic saddles s0+ and s0- can be studied by means of a convergent improper integral that is often called the Melnikov integral. The goal of this paper is to study the applicability of this formula in more general situations, for instance, when the singularities s0± are semi-hyperbolic or even nilpotent. We will show that in some of these cases, the improper integral is no longer convergent but nevertheless, under convenient hypothesis, there is a kind of residue that provides the desired information. Our main result, Theorem A, expands the scope of situations in which we can study the breaking of homoclinic or heteroclinic connections. We show that this is indeed the case by analysing three different examples: a heteroclinic connection between nodes, a heteroclinic connection between semi-hyperbolic saddles at infinity and a homoclinic connection in a non-elementary singularity at infinity. As an application of Theorem A we obtain a general result aimed at studying the breaking of hemicycles and we present several results to analyse the perturbation of unbounded polycycles within a quadratic unfolding that is versal.
Ajuts:	Agencia Estatal de Investigación PID2021-125625NB-I00 Agencia Estatal de Investigación PID2022-136613NB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-01015
Nota:	Altres ajuts: acords transformatius de la UAB
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Saddle connection ; Separation function ; Polycycle
Publicat a:	Qualitative theory of dynamical systems, Vol. 24, Issue 5 (October 2025) , art. 227, ISSN 1662-3592

DOI: 10.1007/s12346-025-01379-8

40 p, 817.4 KB

El registre apareix a les col·leccions:
Articles > Articles de recerca
Articles > Articles publicats