1.
 14 p, 332.1 KB Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones / 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 D. S. (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
2.
 13 p, 669.2 KB Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems / Braun, Francisco (Universidade Federal de Sâo Carlos Rod(Brasil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (UFSCar(Brazil). Department of Physics, Chemistry and Mathematics) In this paper we completely characterize trivial isochronous centers of degrees 5 and 7. Precisely, we provide formulas, up to linear change of coordinates, for the Hamiltonian H of the isochronous centers such that H =(f_1^2 f_2^2)/2 has degrees 6 and 8, and f = (f_1, f_2): R^2 R^2 is a polynomial map with D f = 1 and f(0,0) = (0,0). 2016 - 10.3934/dcds.2016029 Discrete and continuous dynamical systems. Series A, Vol. 36 Núm. 10 (2016) , p. 5245-5255
3.
 14 p, 650.4 KB Limit cycles for discontinuous quadratic differential systems with two zones / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (UFSCar(Brazil). Department of Physics, Chemistry and Mathematics) In this paper we study the maximum number of limit cycles given by the averaging theory of first order for discontinuous differential systems, which can bifurcate from the periodic orbits of the quadratic isochronous centers ˙x = −y + x2, ˙y = x + xy and ˙x = −y + x2 − y2, y˙ = x + 2xy when they are perturbed inside the class of all discontinuous quadratic polynomial differential systems with the straight line of discontinuity y = 0. [...] 2014 - 10.1016/j.jmaa.2013.12.031 Journal of mathematical analysis and applications, Vol. 413 Núm. 2 (2014) , p. 763-775
4.
 9 p, 763.1 KB Limit cycles for a class of discontinuous generalized Liénard polynomial differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (UFSCar(Brazil). Department of Physics, Chemistry and Mathematics) We divide R2 in l sectors S1, . . . , Sl, with l > 1 even. We define in R2 a discontinuous differential system such that in each sector Sk, for k = 1, . . . , l, is defined a smooth generalized Lienard polynomial differential equation ¨x + fi(x) ˙x + gi(x) = 0, i = 1, 2 alternatively, where fi and gi are polynomials of degree n−1 and m respectively. [...] 2013 Electronic journal of differential equations, Vol. 2013 Núm. 195 (2013) , p. 1-8
5.
 16 p, 309.4 KB Limit Cycles for a Generalized Kukles Polynomial Differential Systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (Universidade Federal do ABC (Brazil). Centro de Matematica, Computação e Cognição) We study the limit cycles of generalized Kukles polynomial differential systems using averaging theory of first and second order. 2011 - 10.1016/j.na.2010.09.064 Nonlinear Analysis : Theory, Methods and Applications, Vol. 74 (2011) , p. 1261-1271
6.
 21 p, 834.8 KB Averaging theory for discontinuous piecewise differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (Universidade Federal de Sao Carlos (Brazil). Departamento de Física, Química e Matematica) ; Novaes, Douglas D. (Universidade Estadual de Campinas (Brazil). Departamento de Matematica) We develop the averaging theory of first and second order for studying the periodic solutions of discontinuous piecewise differential systems in arbitrary dimension and with an arbitrary number of systems with the minimal conditions of differentiability. [...] 2015 - 10.1016/j.jde.2015.01.022 Journal of differential equations, Vol. 258 (2015) , p. 4007-4032

Vea también: autores con nombres similares
1 Mereu, A.