New Publications:

A. Korobeinikov, M. Caubergh, J. T. Lázaro, J. Sardanyés.   NEW 2020-03-26
Extended Abstracts Spring 2018 (Singularly perturbed systems, multiscale phenomena and hysteresis: theory and applications).
Birhäuser, 2019.
 [Abstract]

J. Ginoux, J. Llibre, K. Tchizawa.   NEW 2020-03-26
Canards existence in the Hindmarsh-Rose model.
In Research Perspectives CRM Barcelona, Summer 2018, 169-175. Springer, 2019. [DOI]
 [Preprint] [Abstract]

L. F. d. S. Gouveia, J. Torregrosa.   NEW 2020-03-24
The local cyclicity problem. Melnikov method using Lyapunov constants.
Preprint. March, 2020.
 [Abstract]

A. Garijo, H. Jang, S. M. Marotta.   NEW 2020-03-24
Generalized rings around the McMullen domain.
Qual. Theory Dyn. Syst., 18, 233-264, 2019. [DOI]
 [Abstract]

J. Llibre.   NEW 2020-03-24
Limit cycles in continuous and discontinuous piecewise linear differential systems with two pieces separated by a straight line.
Bul. Acad. Ştiinţe Repub. Mold. Mat., 2, 3-12, 2019.
 [Preprint] [Abstract]

J. Llibre, C. Valls.   NEW 2020-03-24
Phase portraits of uniform isochronous centers with homogeneous nonlinearities.
Preprint. March, 2020.
 [Abstract]

M. R. Cândido, J. Llibre, C. Valls.   NEW 2020-03-24
Non-existence, existence, and uniqueness of limit cycles for a generalization of the Van der Pol-Duffing and the Rayleigh-Duffing oscilators.
Phys. D, 407, 132458:1-4, 2020. [DOI]
 [Preprint] [Abstract]

J. Llibre, Y. P. Martinez Mancilla, C. Valls.   NEW 2020-03-24
Limit cycles bifurcating of Kolmogorov systems in R^2 and in R^3.
Preprint. March, 2020.
 [Abstract]

J. Ginoux, J. Llibre, C. Valls.   NEW 2020-03-24
Dynamics and Darboux integrability of the $D_2$ polynomial vector fields of degree 2 in $R^3$.
Preprint. March, 2020.
 [Abstract]

A. Buica, A. Gasull.   NEW 2020-03-24
Many periodic solutions for a second order cubic periodic differential equation.
Preprint. March, 2020.
 [Preprint] [Abstract]

L. F. d. S. Gouveia, J. Torregrosa.   NEW 2020-03-18
Local cyclicity in low degree planar piecewise polynomial vector fields.
Preprint. March, 2020.
 [Abstract]

A. Vajdi, D. Juher, J. Saldaña, C. Scoglio.   NEW 2020-03-05
A multilayer temporal network model for STD spreading accounting for permanent and casual partners.
Sci. Rep., 10, 3846:1-12, 2020.
 [Abstract] [Full PDF]

M. R. A. Gouveia, J. Llibre, L. A. Roberto.   NEW 2020-03-05
Phase portraits of the quadratic polynomial Liénard differential systems.
Proc. Roy. Soc. Edinburgh Sect. A, 1-15, 2020. [DOI]
 [Preprint] [Abstract]

J. L. G. Guirao, J. Llibre, J. A. Vera, B. A. Wade.   NEW 2020-03-05
Periodic solutions and their stability for some perturbed Hamiltonian systems.
Preprint. March, 2020.
 [Abstract]

J. Llibre, Y. Tian.   NEW 2020-03-05
Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree $-4$.
Preprint. March, 2020.
 [Abstract]

M. Corbera, C. Valls.   NEW 2020-03-03
Polynomial Hamiltonian systems of degree 3 with nilpotent saddles.
Preprint. March, 2020.
 [Abstract]

M. Corbera, C. Valls.   NEW 2020-03-03
Hamiltonian nilpotent saddles of linear plus cubic homogeneous polynomial vector fields.
Preprint. March, 2020.
 [Abstract]

M. Corbera, C. Valls.   NEW 2020-03-03
Nilponent saddles of linear plus cubic homogeneous polynomial reversible vector fields.
Preprint. March, 2020.
 [Abstract]

M. Corbera, C. Valls.   NEW 2020-03-03
Global phase portraits of Z2-Symmetric planar polynomial Hamiltonian systems of degree three with a nilpotent saddle at the origin.
Internat. J. Bifur. Chaos Appl. Sci. Engrg., 30(1), 2050006:1-30, 2020. [DOI]
 [Preprint] [Abstract]

J. Giné, L. F. d. S. Gouveia, J. Torregrosa.   NEW 2020-03-02
Lower bounds for the local cyclicity for families of centers.
Preprint. March, 2020.
 [Abstract]

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]
 [Preprint] [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.
Rev. Mat. Iberoam., 36(1), 2020. [DOI]
 [Preprint] [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.
 [Preprint] [Abstract]