New Publications:

J. L. Cardoso, J. Llibre, D. D. Novaes, D. J. Tonon.   NEW 2020-02-11
Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields.
Dyn. Syst., 1-25, 2020. [DOI]
 [Abstract]

J. Llibre, C. Valls.   NEW 2020-02-11
Rational limit cycles on Abel equations.
Preprint. February, 2020.
 [Abstract]

L. Jiménez-Lara, J. Llibre.   NEW 2020-02-11
The free Euler equations revisited.
Preprint. February, 2020.
 [Abstract]

T. Li, J. Llibre.   NEW 2020-02-11
Phase portraits of Bernoulli quadratic systems and a bibliographical survey on quadratic systems.
Preprint. February, 2020.
 [Abstract]

I. Basak, J. Llibre.   NEW 2020-02-11
Dynamics of two Einstein-Friedmann cosmological models.
Preprint. February, 2020.
 [Abstract]

I. A. García, J. Giné, J. Llibre, S. Maza.   NEW 2020-02-11
Vanishing set of inverse Jacobi multipliers and attractor/repulsor sets.
Preprint. February, 2020.
 [Abstract]

J. Llibre, P. Pedregal.   NEW 2020-02-07
Hilbert's 16th problem. When differential systems meet variational principles.
Preprint. February, 2020.
 [Preprint] [Abstract]

L. F. d. S. Gouveia.   NEW 2020-01-14
Limit cycles of small amplitude in polynomial and piecewise polynomial planar vector fields.
PhD thesis, Universitat Autònoma de Barcelona, Bellaterra, January, 2020.
 [Abstract]

H. Chen, J. Llibre, Y. Tang.   NEW 2020-01-14
The limit cycles of the Higgins-Selkov systems.
Preprint. January, 2020.
 [Abstract]

F. Güngör, J. Llibre, C. Pantazi.   NEW 2020-01-14
Darboux integrability and dynamics of the Basener-Ross population model.
Preprint. January, 2020.
 [Abstract]

R. Benterki, J. Llibre.   NEW 2020-01-14
The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems.
Preprint. January, 2020.
 [Abstract]

J. Llibre, C. Valls.   NEW 2020-01-14
On the configurations of the singular points and their topological indices for the spatial quadratic polynomial differential systems.
Preprint. January, 2020.
 [Abstract]

L. F. d. S. Gouveia, J. Torregrosa.   NEW 2020-01-03
Lower bounds for the local cyclicity of centers using high order developments and parallelization.
Preprint. January, 2020.
 [Preprint] [Abstract]

A. Cima, A. Gasull, F. Mañosas.   NEW 2019-12-20
Around some extensions of Casas-Alvero conjecture for non-polynomial functions.
Preprint. December, 2019.
 [Preprint] [Abstract]

A. Gasull, C. Valls.   NEW 2019-12-20
Discrete Melnikov functions.
Preprint. December, 2019.
 [Preprint] [Abstract]

J. Llibre, R. D. S. Oliveira, Y. Zhao.   NEW 2019-12-20
On the birth and death of algebraic limit cycles in quadratic differential systems.
Preprint. December, 2019.
 [Abstract]

A. Cima, A. Gasull, V. Mañosa.   NEW 2019-12-20
A dynamic Parrondo's paradox for continuous seasonal systems.
Preprint. December, 2019.
 [Preprint] [Abstract]

J. Llibre, D. D. Novaes, I. O. Zeli.   NEW 2019-12-20
Limit cycles of piecewise polynomial perturbations of higher dimensional lineal differential systems.
Preprint. December, 2019.
 [Abstract]

C. Li, J. Llibre.   NEW 2019-12-20
The cyclicity of the period annulus of a reversible quadratic system.
Preprint. December, 2019.
 [Abstract]

V. Ramírez.   NEW 2019-12-10
Qualitative theory of differential equations in the plane and in the space, with emphasis on the center-focus problem and on the lotka-Volterra systems.
PhD thesis, Universitat Autònoma de Barcelona, Bellaterra, November, 2019.
 [Abstract]

J. Llibre, A. Sá.   NEW 2019-12-05
Minimal set of periods for continuous self-maps of a bouquet of circles.
Preprint. December, 2019.
 [Abstract]

J. Llibre, D. J. Tonon, M. Q. Velter.   NEW 2019-12-05
Crossing periodic orbits via first integrals.
Preprint. December, 2019.
 [Abstract]

R. Benterki, J. Llibre.   NEW 2019-12-05
Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points.
Preprint. December, 2019.
 [Abstract]

A. Cima, A. Gasull, V. Mañosa.   NEW 2019-12-05
Phase portraits of random planar homogeneous vector fields.
Preprint. December, 2019.
 [Preprint] [Abstract]

M. R. A. Gouveia, J. Llibre.   NEW 2019-12-05
Periods of periodic homeomorphisms of pinched surfaces with one or two branching points.
Houston J. Math., 45(4), 1227-1243, 2019.
 [Abstract]

J. Llibre, C. Valls.   NEW 2019-11-15
On the singularities of the planar cubic polynomial differential systems and the Euler Jacobi formula.
Preprint. November, 2019.
 [Abstract]

J. Llibre, R. O. Ramírez, V. Ramírez.   NEW 2019-11-15
Integrability of a class of N-dimensional Lotka-Volterra and Kolmogorov systems.
Preprint. November, 2019.
 [Abstract]

B. Coll, A. Gasull, R. Prohens.   NEW 2019-11-15
Asymptotic dynamics of a difference equation with a parabolic equilibrium.
Preprint. November, 2019.
 [Preprint] [Abstract]

A. Feddaoui, J. Llibre, A. Makhlouf.   NEW 2019-11-15
Periodic solutions for a class of Duffing differential equations.
Moroccan J. of Pure and Appl. Anal., 5(1), 86-103, 2019. [DOI]
 [Preprint] [Abstract]

M. Corbera, C. Valls.   NEW 2019-11-11
On centered co-circular central configurations of the n-body problem.
J. Dyn. Diff. Equat., 31, 2053-2060, 2019.
 [Preprint] [Abstract]

A. Garijo, X. Jarque.   NEW 2019-11-11
The secant map applied to a real polynomial with multiple roots.
To appear in Discrete Contin. Dyn. Syst.
 [Preprint] [Abstract]

F. Ikhouane, V. Mañosa, G. Pujol.   NEW 2019-11-11
Minor loops of the Dahl and LuGre models.
Appl. Math. Model., 77, 1679-1690, 2020. [DOI]
 [Preprint] [Abstract]

L. F. d. S. Gouveia, J. Torregrosa.   NEW 2019-11-11
24 crossing limit cycles in only one nest for piecewise cubic systems.
Appl. Math. Lett., 103, 106189, 2020. [DOI]
 [Preprint] [Direct Shared Link] [Abstract]

M. Corbera, J. Llibre, P. Yuan.   NEW 2019-11-11
On the convex central configurations of the symmetric (l+2)-body problem.
Preprint. November, 2019.
 [Abstract]

F. Gao, J. Llibre.   NEW 2019-11-11
Global dynamics of the Horava-Lifshitz cosmology with non-zero curvature.
Preprint. November, 2019.
 [Abstract]

J. Llibre, X. Zhang.   NEW 2019-11-05
A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems.
Preprint. November, 2019.
 [Abstract]

J. D. García Saldaña, A. Gasull, H. Giacomini.   NEW 2019-11-05
A new approach for the study of limit cycles.
Preprint. November, 2019.
 [Preprint] [Abstract]