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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
2 documents
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30 p, 504.7 KB |
Phase portraits of random planar homogeneous vector fields
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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)
In this paper, we study the probability of occurrence of phase portraits in the set of random planar homogeneous polynomial vector fields, of degree n. In particular, for n= 1, 2, 3, we give the complete solution of the problem; that is, we either give the exact value of each probability of occurrence or we estimate it by using the Monte Carlo method. [...]
2021 - 10.1007/s12346-020-00437-7
Qualitative theory of dynamical systems, Vol. 20, Issue 1 (April 2021) , art. 3
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14 p, 663.8 KB |
On Poncelet's maps
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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 Matemàtica Aplicada III)
Given two ellipses, one surrounding the other one, Poncelet introduced a map P from the exterior one to itself by using the tangent lines to the interior ellipse. This procedure can be extended to any two smooth, nested and convex ovals and we call these types of maps, Poncelet's maps. [...]
2010 - 10.1016/j.camwa.2010.06.027
Computers and Mathematics with Applications, Vol. 60, Issue 5 (September 2010) , p. 1457-1464
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