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52 p, 1.1 MB |
Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e Computação) ;
Rodrigues, Camila A. B. (Universidade Federal de Santa Catarina. Departamento de Matemática (Brazil))
Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normalforms for the quadratic systems in QS3. [...]
2021
Electronic journal of differential equations, Vol. 2021, Issue 69 (2021) , p. 1-52
2 documents
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129 p, 4.9 MB |
Geometric and algebraic classification of quadratic differential systems with invariant hyperbolas
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Oliveira, Regilene (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação) ;
Rezende, Alex C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ;
Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
Let QSH be the whole class of non-degenerate planar quadratic differential systems possessing at least one invariant hyperbola. We classify this family of systems, modulo the action of the group of real affine transformations and time rescaling, according to their geometric properties encoded in the configurations of invariant hyperbolas and invariant straight lines which these systems possess. [...]
2017
Electronic journal of differential equations, Vol. 2017, Issue 295 (2017) , p. 1-122
2 documents
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16 p, 666.6 KB |
Limit cycles for two classes of control piecewise linear differential systems
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Oliveira, Regilene (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil)) ;
Rodrigues, Camila A. B. (Universidade Federal de Santa Catarina. Departamento de Matemática (Brazil))
We study the bifurcation of limit cycles from the periodic orbits of 2n-dimensional linear centers x˙ = A0x when they are perturbed inside classes of continuous and discontinuous piecewise linear differential systems of control theory of the form x˙ = A0x+ ε(Ax+ ϕ(x) b), where ϕ is a continuous or discontinuous piecewise linear function, A0 is a 2n×2n matrix with only purely imaginary eigenvalues, ε is a small parameter, A is an arbitrary 2n×2n matrix, and b is an arbitrary vector of Rn.
2020 - 10.1007/s40863-020-00163-7
São Paulo Journal of Mathematical Sciences, Vol. 14, Issue 1 (June 2020) , p. 49-65
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14 p, 332.1 KB |
Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones
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Itikawa, Jackson (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil)) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Mereu, Ana Cristina (Universidade Federal de São Carlos. Departamento de Física, Química e Matemática (Brazil)) ;
Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil))
We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. [...]
2017 - 10.3934/dcdsb.2017136
Discrete and continuous dynamical systems. Series B, Vol. 22, Issue 9 (November 2017) , p. 3259-3272
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