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Articles 38 registres trobats  1 - 10següentfinal  anar al registre:
1.
18 p, 334.8 KB Limit cycles of linear vector fields on (S2)m ×Rn / Cufí Cabré, Clara (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
It is well known that linear vector fields defined in Rn cannot have limit cycles, but this is not the case for linear vector fields defined in other manifolds. We study the existence of limit cycles bifurcating from a continuum of periodic orbits of linear vector fields on manifolds of the form (S2)m × Rn when such vector fields are perturbed inside the class of all linear vector fields. [...]
2023 - 10.2140/pjm.2023.324.249
Pacific Journal of Mathematics, Vol. 324, Issue 2 (June 2023) , p. 249-263  
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2.
22 p, 506.0 KB Contact geometry and isosystolic inequalities / Alvarez Paiva, Juan Carlos (Université de Lille. Laboratoire Paul Painlevé) ; Balacheff, Florent Nicolas (Université de Lille. Laboratoire Paul Painlevé)
A long-standing open problem asks whether a Riemannian metric on the real projective space with the same volume as the canonical metric carries a periodic geodesic whose length is at most π. A contact-geometric reformulation of systolic geometry and the use of canonical perturbation theory allow us to solve a parametric version of this problem: if g s is a smooth, constant-volume deformation of the canonical metric that is not formally trivial, the length of the shortest periodic geodesic of the metric g s attains π as a strict local maximum at s = 0. [...]
2014 - 10.1007/s00039-014-0250-2
Geometric and Functional Analysis, Vol. 24, Issue 2 (April 2014) , p. 648-669  
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3.
23 p, 413.2 KB Limit cycles of a class of discontinuous piecewise differential systems separated by the curve y = xn via averaging theory / Guo, Zhifei (Sichuan University. School of Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Recently there is increasing interest in studying the limit cycles of the piecewise differential systems due to their many applications. In this paper we prove that the linear system ẋ = y, ẏ = -x, can produce at most seven crossing limit cycles for n ≥ 4 using the averaging theory of first order, where the bounds ≤ 4 for n ≥ 4 even and the bounds ≤ 7 for n ≥ 5 odd are reachable, when it is perturbed by discontinuous piecewise polynomials formed by two pieces separated by the curve y = xn (n ≥ 4), and having in each piece a quadratic polynomial differential system. [...]
The study of the limit cycles of planar differential systems is one of the main problems in the qualitative theory of differential systems. These last years a big interest appeared for studying the limit cycles of the piecewise differential systems due to their many applications. [...]
2022 - 10.1142/S0218127422501875
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 12 (September 2022) , art. 2250187  
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4.
12 p, 350.7 KB Non-equivalence between the Melnikov and the averaging methods for nonsmooth differential systems / Guo, Zhifei (Sichuan University. School of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
It is known that for smooth differential systems in the plane R2 the Melnikov and the averaging methods for studying the limit cycles produce the same results. Here we prove that this is not the case for nonsmooth differential systems in the plane. [...]
2022 - 10.1007/s12346-022-00643-5
Qualitative theory of dynamical systems, Vol. 21, Issue 4 (December 2022) , art. 114  
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5.
13 p, 856.4 KB Limit cycles of piecewise polynomial differential systems with the discontinuity line xy = 0 / Li, Tao (Southwestern University of Finance and Economics. School of Economic Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the maximum number of limit cycles bifurcating from the periodic orbits of the center x. = −y((x + y)/2), y. = x((x + y)/2) with m ≥ 0 under discontinuous piecewise polynomial (resp. [...]
2021 - 10.3934/cpaa.2021136
Communications on pure & applied analysis, Vol. 20, Issue 11 (November 2021) , p. 3887-3909  
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6.
26 p, 910.3 KB Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary / Li, Tao (Sichuan University. Department of Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Continuing the investigation for the piecewise polynomial perturbations of the linear center ẋ = −y, ẏ = x from Buzzi et al. (2018) for the case where the switching boundary is a straight line, in this paper we allow that the switching boundary is non-regular, i. [...]
2021 - 10.1016/j.physd.2021.132855
Physica D. Nonlinear phenomena, Vol. 419 (May 2021) , p. 132855  
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7.
16 p, 712.0 KB On the 16th Hilbert problem for discontinuous piecewise polynomial Hamiltonian systems / Li, Tao (Sichuan University. Department of Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the maximum number of limit cycles of the discontinuous piecewise differential systems with two zones separated by the straight line y = 0, in y ≥ 0 there is a polynomial Hamiltonian system of degree m, and in y ≤ 0 there is a polynomial Hamiltonian system of degree n. [...]
2021 - 10.1007/s10884-021-09967-3
Journal of dynamics and differential equations, Vol. 35 (March 2021) , p. 87-102  
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8.
9 p, 569.4 KB Bifurcation of limit cycles from a two-dimensional center inside Rn / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba. Department of Mathematics (Algeria))
We study the bifurcation of limit cycles from the periodic orbits of a linear differential system in Rn perturbed inside a class of piecewise linear differential systems, which appears in a natural way in control theory. [...]
2010 - 10.1016/j.na.2009.08.022
Nonlinear Analysis : Theory, Methods and Applications, Vol. 72, Issue 3-4 (February 2010) , p. 1387-1392  
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9.
31 p, 575.7 KB Limit cycles of piecewise polynomial perturbations of higher dimensional lineal differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática (Brazil)) ; Zeli, Iris O. (Instituto Tecnológico de Aeronáutica. Departamento de Matemática (Brazil))
The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed non-autonomous n-dimensional discontinuous piecewise smooth differential system. [...]
2020 - 10.4171/rmi/1131
Revista Matemática Iberoamericana, Vol. 36, Núm. 1 (2020) , p. 291-318  
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10.
18 p, 893.2 KB Periodic solutions for a class of Duffing differential equations / Feddaoui, Amina (University of Annaba. Department of Mathematics (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba. Department of Mathematics (Algeria))
We provide sufficient conditions for the existence of periodic solutions in the class of Duffing differential equations x" + c(t)x' + a(t)x + b(t)x3 = h(t,x), where the functions a(t), b(t), c(t) and h(t,x) are C2 and T-periodic in the variable t.
2019 - 10.2478/mjpaa-2019-0007
Moroccan Journal of Pure and Applied Analysis, Vol. 5, Issue 1 (June 2019) , p. 86-103
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Articles : 38 registres trobats   1 - 10següentfinal  anar al registre:
Documents de recerca 1 registres trobats  
1.
132 p, 1.2 MB Dois métodos para a investigação de ciclos limites que bifurcam de centros / Rezende, Alex Carlucci ; Oliveira, Regilene Delazari dos Santos, dir.
Um dos mais investigados problemas na teoria qualitativa dos sistemas dinâmicos no plano é o XVI problema de Hilbert que trata dos ciclos limites. Mais precisamente, a segunda parte do referido problema questiona sobre o número máximo de ciclos limites de um sistema diferencial polinomial plano de grau n. [...]
One of the most investigated problems in the qualitative theory of dynamical systems in the plane is the XVI Hilbert's problem which deals with limit cycles. More precisely, the second part of the problem asks about the maximum number of limit cycles of a polynomial differential system of degree n. [...]
2011  
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