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Topological Moduli Space for Germs of Holomorphic Foliations
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Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Mattei, Jean-François (Institut de Mathématiques de Toulouse) ;
Salem, Eliane (Sorbonne Université. Institut de Mathématiques de Jussieu-Paris Rive Gauche)
This work deals with the topological classification of germs of singular foliations on (ℂ2,0). Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices, and the projective holonomy representations and we compute the moduli space of topological classes in terms of the cohomology of a new algebraic object that we call group-graph. [...]
2020 - 10.1093/imrn/rny244
International Mathematics Research Notices, Vol. 2020, Issue 23 (November 2020) , p. 9228-9292
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34 p, 471.7 KB |
Stability index of linear random dynamical systems
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Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution. In particular, for the n dimensional case, the zero solution is globally asymptotically stable if and only if this stability index is n. [...]
2021 - 10.14232/ejqtde.2021.1.15
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2021, Issue 15 (2021) , p. 1-27
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11 p, 246.0 KB |
Qualitative behaviour analysis of feedback-controlled Buck-Boost power converters thru three different techniques
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Sosa, Keiver (Universidad de Los Andes. Doctorado en Ciencias Aplicadas (Venezuela)) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Spinetti-Rivera, Mario (Universidad de Los Andes. Departamento de Sistemas de Control (Venezuela)) ;
Colina-Morles, Eliezer (Universidad de Cuenca. Departamento de Ingeniería Eléctrica, Electrónica y Telecomunicaciones (Ecuador))
This work is based on the comparison of three techniques for analyzing the qualitative behaviour of nonlinear dynamic systems, including the study of their finite and infinite equilibrium points. The qualitative techniques used are: the direct method of Lyapunov, The theorems of Dickson and Perko for second order quadratic differential systems and the linearization around finite equilibrium points. [...] Este trabajo se basa en la comparación de tres técnicas de análisis del comportamiento cualitativo de sistemas dinámicos no lineales, incluyendo el estudio de los puntos de equilibrio finitos e infinitos. [...]
2018
Revista Politécnica, Vol. 42, Núm. 1 (Agosto-Octubre 2018) , p. 7-16
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