Preprints:

S. Li, J. Llibre.   NEW 2019-09-23
Phase portraits of planar piecewise linear refracting systems: focus-Saddle case.
Preprint. September, 2019.
 [Abstract]

A. Bakhshalizadeh, J. Llibre.   NEW 2019-09-23
The Hilbert number of some classes of differential equations on the torus.
Preprint. September, 2019.
 [Abstract]

J. Llibre, V. F. Sirvent.   NEW 2019-09-06
Periods of holomorphic maps on compact riemann surfaces and product of spheres.
Preprint. September, 2019.
 [Abstract]

J. J. Jimenez Ruiz, J. Llibre, J. C. Medrado.   NEW 2019-09-04
Crossing limit cycles for piecewise linear differential centers separated by a reducible cubic curve.
Preprint. September, 2019.
 [Abstract]

S. Li, C. Liu, J. Llibre.   NEW 2019-09-04
The planar discontinuous piecewise linear refracting systems have at most one limit cycle.
Preprint. September, 2019.
 [Abstract]

A. Bakhshalizadeh, J. Llibre.   NEW 2019-09-04
Phase portraits of a class of cubic systems with an ellipse and a straight line as invariant algebraic curves.
Preprint. September, 2019.
 [Abstract]

M. Alberich-Carramiñana, A. Ferragut, J. Llibre.   NEW 2019-09-04
Quadratic planar differential systems with algebraic limit cycles via quadratic plane Cremona maps.
Preprint. September, 2019.
 [Abstract]

J. Llibre, C. Valls.   NEW 2019-09-04
Configurations of the topological indices of the planar polynomial differential systems of degree $(1,m)$.
Preprint. September, 2019.
 [Abstract]

T. Chen, L. Huang, J. Llibre.   NEW 2019-09-04
Non-existence and uniqueness of limit cycles for a class of $3$-dimensional piecewise linear differential systems.
Preprint. September, 2019.
 [Abstract]

F. Gao, J. Llibre.   NEW 2019-09-04
Global dynamics of the Horava-Lifshitz cosmological system.
Preprint. September, 2019.
 [Abstract]

N. Kruff, J. Llibre, C. Pantazi, S. Walcher.   NEW 2019-09-04
Invariant algebraic surfaces of polynomial vector fields in dimension three.
Preprint. September, 2019.
 [Abstract]

A. F. Fonseca, J. Llibre, L. F. Mello.   NEW 2019-07-22
Limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points.
Preprint. July, 2019.
 [Abstract]

J. C. Artés, J. Llibre, D. Schlomiuk, N. Vulpe.   NEW 2019-07-22
Global topological configurations of singularities for the whole family of quadratic differential systems.
Preprint. July, 2019.
 [Abstract]

D. Marín, J. Villadelprat.   NEW 2019-07-22
Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: local setting.
Preprint. July, 2019.
 [Preprint] [Abstract]

A. Gasull, J. Giné, C. Valls.   NEW 2019-07-22
Highest weak focus order for trigonometric Liénard equations.
Preprint. July, 2019.
 [Preprint] [Abstract]

R. Euzébio, J. Llibre, D. J. Tonon.   NEW 2019-07-22
Lower bounds for the number of limit cycles in a generalized Rayleigh-Liénard oscillator.
Preprint. July, 2019.
 [Abstract]

A. Cima, A. Gasull, F. Mañosas.   NEW 2019-06-28
A note on the Lyapunov and Period constants.
Preprint. June, 2019.
 [Preprint] [Abstract]

D. Rojas.   NEW 2019-06-26
Resonance of bounded isochronous oscillators.
Preprint. June, 2019.
 [Preprint] [Abstract]

J. Llibre, C. Valls.   NEW 2019-06-25
Configurations of the topological indices of the planar polynomial differential systems of degree (2,m).
Preprint. June, 2019.
 [Abstract]

F. Gao, J. Llibre.   NEW 2019-06-25
Periodic orbits of the two fixed centers problem with a variational gravitational field.
Preprint. June, 2019.
 [Abstract]

M. R. Cândido, C. Valls.   NEW 2019-06-12
Zero-Hopf bifurcation in the general van der pol-Duffing equation.
Preprint. June, 2019.
 [Preprint] [Abstract]

A. Algaba, C. García, J. Giné, J. Llibre.
Orbitally universal centers.
Preprint. May, 2019.
 [Abstract]

J. Llibre, T. Salhi.
On the limit cycles surrounding a diagonalizable linear node with homogeneous nonlinearities.
Preprint. May, 2019.
 [Abstract]

J. L. G. Guirao, J. Llibre, W. Gao.
C1 self-maps on some compact manifolds with infinitely many hyperbolic periodic orbits.
Preprint. May, 2019.
 [Abstract]

J. Llibre, A. Nabavi.
Phase portraits of the Selkov model in the Poincaré disc.
Preprint. May, 2019.
 [Abstract]

J. Llibre, M. Mousavi.
Phase portraits of the Higgins-Selkov system.
Preprint. May, 2019.
 [Abstract]

J. Llibre, R. O. Ramírez, V. Ramírez.
On the integrability of vector fields in R^N.
Preprint. May, 2019.
 [Abstract]

G. Cousillas, J. Groisman, J. Xavier.
Topologically Anosov plane homeomorphisms.
Preprint. April, 2019.
 [Preprint] [Abstract]

G. Cousillas.
A fixed point theorem for plane homeomorphisms with the topological shadowing property.
Preprint. April, 2019.
 [Preprint] [Preprint]

J. Llibre, C. Pessoa, J. Donizetti.
Rational first integrals of the Liénard equations: The solution to the Poincaré problem for the Liénard equations.
Preprint. April, 2019.
 [Abstract]

J. Llibre, Y. P. Martinez Mancilla, C. Valls.
On the global dynamics of a three-dimensional forced-damped differential system.
Preprint. April, 2019.
 [Abstract]

A. Cima, A. Gasull, V. Mañosa.
Stability index of linear random dynamical systems.
Preprint. April, 2019.
 [Preprint] [Abstract]

J. Llibre, T. Salhi.
On a class of polynomial differential systems of degree 4: phase portraits and limit cycles.
Preprint. April, 2019.
 [Abstract]

D. Djedid, J. Llibre, A. Makhlouf.
Periodic orbits bifurcating from a Hopf equilibrium of 2-dimensional polynomial Kolmogorov systems of arbitrary degree.
Preprint. April, 2019.
 [Abstract]

J. J. Jimenez Ruiz, J. Llibre, J. C. Medrado.
Crossing limit cycles for a class of piecewise linear differential centers separated by a conic.
Preprint. March, 2019.
 [Abstract]

R. Benterki, J. Llibre.
The limit cycles of piecewise linear differential systems formed by centers and separated by irreducible cubic curves.
Preprint. March, 2019.
 [Abstract]

M. Corbera, J. Llibre.
Spatial convex but non-strictly convex double-pyramidal central configurations of the (2n+2)-body problem.
Preprint. March, 2019.
 [Abstract]

J. Llibre, R. O. Ramírez, N. Sadovskaia.
Integrability in the Liouville sense for complex Hamiltonian systems.
Preprint. March, 2019.
 [Abstract]

L. Barreira, J. Llibre, C. Valls.
Global nilpotent centers of cubic polynomial Hamiltonian systems symmetric with respect to the y-axis.
Preprint. February, 2019.
 [Abstract]

L. Barreira, J. Llibre, C. Valls.
Bounded polynomial vector fields in R^2 and R^n.
Preprint. February, 2019.
 [Abstract]

J. Llibre, Y. P. Martinez Mancilla.
Dynamics of a competitive Lotka-Volterra systems in R^3.
Preprint. January, 2019.
 [Abstract]

J. Llibre, B. D. Lopes, P. R. Silva.
Global phase portraits of the quadratic Riccati differential system.
Preprint. December, 2018.
 [Abstract]

J. Llibre, O. Ramírez.
Gradient systems of harmonic polynomials.
Preprint. December, 2018.
 [Abstract]

J. Llibre, M. A. Teixeira.
Limit cycles in Filippov systems having a circle as switching manifold.
Preprint. December, 2018.
 [Abstract]

J. Llibre, Y. Zhao.
Final evolutions for Lotka-Volterra systems in R3 having a Darboux invariant.
Preprint. December, 2018.
 [Abstract]

J. Llibre, Y. P. Martinez Mancilla.
Dynamics of a family of Lotka-Volterra systems in R^3.
Preprint. December, 2018.
 [Abstract]

J. L. G. Guirao, J. Llibre, W. Gao.
Topological entropy of continuous self-maps on closed surfaces.
Preprint. December, 2018.
 [Abstract]

J. Llibre, R. D. S. Oliveira.
On the limit cycle of a Belousov-Zabotinsky differential systems.
Preprint. December, 2018.
 [Abstract]

J. Llibre, R. D. S. Oliveira, C. A. B. Rodrigues.
Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant.
Preprint. November, 2018.
 [Abstract]

J. Llibre, D. Xiao.
Cubic polynomial Hamiltonian systems with degenerate centers.
Preprint. November, 2018.
 [Abstract]

E. I. Abouelmagd, J. L. G. Guirao, J. Llibre.
The dynamics of the relativistic Kepler problem.
Preprint. October, 2018.
 [Abstract]

J. Giné, J. Llibre.
Generalized Painlevé non-integrability for polynomial differential systems in $C^2$.
Preprint. October, 2018.
 [Abstract]

J. Llibre, L. d. A. S. Menezes.
On the limit cycles of a class of discontinuous piecewise linear differential systems.
Preprint. October, 2018.
 [Abstract]

J. D. García Saldaña, J. Llibre, C. Valls.
Nilpotent global centers of linear systems with cubic homogeneous nonlinearities.
Preprint. October, 2018.
 [Abstract]

L. Barreira, J. Llibre, C. Valls.
Linear type global centers of cubic Hamiltonian systems symmetric with respect to the x-axis.
Preprint. September, 2018.
 [Abstract]

J. Llibre, R. O. Ramírez.
Integrability by separation of variables.
Preprint. September, 2018.
 [Abstract]

J. Llibre, A. Makhlouf.
Zero-Hopf periodic orbits for a Röossler differential system.
Preprint. September, 2018.
 [Abstract]

S. Li, J. Llibre.
On the number of limit cycles in planar discontinuous piecewise linear differential systems of saddle-node type.
Preprint. September, 2018.
 [Abstract]

J. Llibre, A. Nabavi, M. Mousavi.
Limit cycles bifurcating from a family of reversible quadratic centers via averaging theory.
Preprint. August, 2018.
 [Abstract]

J. C. Artés, J. Llibre, D. Schlomiuk, N. Vulpe.
Global topological configurations of singularities for the whole family of quadratic differential systems.
Preprint. August, 2018.
 [Abstract]

T. Chen, J. Llibre.
On the limit cycles of 3-dimensional piecewise linear differential systems.
Preprint. August, 2018.
 [Abstract]

J. Llibre, D. D. Novaes, C. A. B. Rodrigues.
Branching of limit cycles from families of periodic solutions in piecewise differential systems.
Preprint. August, 2018.
 [Abstract]

T. Chen, J. Llibre.
Topological classification of some SD hamiltonian systems.
Preprint. August, 2018.
 [Abstract]

L. P. C. Cruz, J. Torregrosa.
A Bendixson-Dulac theorem for some piecewise systems.
Preprint. July, 2018.
 [Preprint] [Abstract]

A. Garijo, X. Jarque.
Global dynamics of the real secant method.
Preprint. July, 2018.
 [Preprint] [Abstract]

B. Campos, J. Canela, P. Vindel.
Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials.
Preprint. July, 2018.
 [Preprint] [Abstract]

T. Chen, J. Llibre.
Phase portraits and bifurcation diagrams for some Hamiltonian systems with rational potentials.
Preprint. June, 2018.
 [Abstract]

J. Llibre, C. Valls.
A sufficient condition for the real Jacobian conjecture in $\mathbb R^2$.
Preprint. June, 2018.
 [Abstract]

J. Llibre, V. F. Sirvent.
On topological entropy, Lefschetz numbers and Lefschetz zeta functions.
Preprint. June, 2018.
 [Abstract]

J. Llibre, Y. P. Martinez Mancilla, C. Vidal.
Algebraic and topological classification of homogeneous quartic vector fields in the plane.
Preprint. May, 2018.
 [Abstract]

A. Gasull, J. Torregrosa, X. Zhang.
Piecewise linear differential systems with an algebraic line of separation.
Preprint. April, 2018.
 [Preprint] [Abstract]

S. Kassa, J. Llibre, A. Makhlouf.
3-dimensional zero-Hopf bifurcation via averaging theory.
Preprint. April, 2018.
 [Abstract]

T. Chen, J. Llibre, S. Li.
Phase portraits and bifurcation diagram of the Gray-Scott model.
Preprint. March, 2018.
 [Abstract]

M. R. Cândido, J. Llibre, C. Valls.
Phase portraits of a class of van der Pol-Duffing Liénard differential equations.
Preprint. February, 2018.
 [Abstract]

A. García, J. Llibre.
Existence of periodic solutions for a class of second order ordinary differential equations.
Preprint. February, 2018.
 [Abstract]

S. Li, J. Llibre.
On the existence and uniqueness of limit cycles for continuous piecewise-linear Liénard differential systems with three zones.
Preprint. February, 2018.
 [Abstract]

M. F. S. Lima, J. Llibre.
Double zero-Hopf bifurcation in a four-dimensional hyperchaotic system.
Preprint. February, 2018.
 [Abstract]

M. R. Cândido, J. Llibre, C. Valls.
Phase portraits of the Rayleight-Duffing oscillator with positive linear stiffness and linear damping.
Preprint. January, 2018.
 [Abstract]

J. Llibre, A. Makhlouf.
On some periodic orbits of the fourth-order differential equation $u′′′′+q u′′+ p u = \epsilon f(u,u′,u′′,u′′′)$.
Preprint. January, 2018.
 [Abstract]

J. Llibre, C. Valls.
Weierstrass integrability of complex differential equations.
Preprint. January, 2018.
 [Abstract]

J. Llibre, D. D. Novaes, I. O. Zeli.
Limit cycles bifurcating from discontinuous polynomial perturbations of higher dimensional linear differential systems.
Preprint. January, 2018.
 [Abstract]

J. Llibre.
On the centers of cubic polynomial differential systems with four invariant straight lines.
Preprint. December, 2017.
 [Abstract]

Ll. Alsedà, L. Bordignon, J. Groisman.
Topological entropy, sets of periods and transitivity for graph maps.
Preprint. December, 2017.
 [Preprint] [Abstract]

J. Llibre, B. D. Lopes, J. R. Moraes.
Periodic solutions of continuous third-order differential equations with piecewise polynomial nonlinearities.
Preprint. November, 2017.
 [Abstract]

M. Han, J. Llibre, Y. Tian.
On the zero-Hopf bifurcatIon of the Lotka-Volterra systems in $\mathbb R^3$.
Preprint. November, 2017.
 [Abstract]

J. Llibre, J. A. Vera.
Periodic solutions and their stability for some perturbed Hamiltonian systems.
Preprint. November, 2017.
 [Abstract]

N. Fagella, L. Keen.
Dynamics of purely meromorphic functions of bounded type.
Preprint. November, 2017.
 [Preprint] [Abstract]

S. Li, J. Llibre.
On the limit cycles for discontinuous piecewise linear differential systems.
Preprint. October, 2017.
 [Abstract]

J. Llibre, C. Valls.
Centers of planar generalized Abel equations.
Preprint. October, 2017.
 [Abstract]

J. Llibre, A. Murza, C. Valls.
We prove a conjecture on the integrability of Liénard systems.
Preprint. October, 2017.
 [Abstract]

D. Djedid, J. Llibre, A. Makhlouf.
4-dimensional Hopf bifurcation via averaging theory.
Preprint. October, 2017.
 [Abstract]

C. A. Buzzi, J. Llibre, R. Pazim.
On the dynamics of the Euler equations on SO(4).
Preprint. October, 2017.
 [Abstract]

J. Llibre, C. Valls.
Global qualitative dynamics of the brusselator system.
Preprint. September, 2017.
 [Abstract]

J. Llibre, A. Murza.
Polynomial vector fields on the Clifford torus.
Preprint. July, 2017.
 [Abstract]

J. Itikawa, J. Llibre.
New families of planar Hamiltonian systems having global centers.
Preprint. June, 2017.
 [Abstract]

J. Llibre, L. d. A. S. Menezes.
The Markus–Yamabe conjecture does not hold for piecewise discontinuous linear differential systems separated by one straight line.
Preprint. June, 2017.
 [Abstract]

A. Cima, S. Zafar.
Invariant fibrations for some birational maps of $\mathbb C^2$.
Preprint. May, 2017.
 [Abstract]

J. Llibre, A. Murza, A. E. Teruel.
First integrals of a class of n-dimensional Lotka-Volterra differential systems.
Preprint. May, 2017.
 [Abstract]

J. Llibre, A. Makhlouf.
Limit cycles of nonlinear torsional vibration system via averaging theory.
Preprint. March, 2017.
 [Abstract]

R. Benterki, J. Llibre.
The centers and their cyclicity for a class of polynomial differential systems of degree 7.
Preprint. April, 2017.
 [Abstract]

L. Barreira, J. Llibre, C. Valls.
Integrability and zero-Hopf bifurcation in the Sprott A system.
Preprint. April, 2017.
 [Abstract]

J. Llibre, D. Xiao.
On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems.
Preprint. March, 2017.
 [Abstract]

M. R. Cândido, J. Llibre.
On the averaging theory for computing periodic solutions and its applications.
Preprint. February, 2017.
 [Abstract]

J. Llibre, A. Makhlouf.
On the periodic solutions of the relativistic driven harmonic oscillator.
Preprint. January, 2017.
 [Abstract]

J. Llibre, J. C. Medrado, O. Ramírez.
Limit cycles of planar piecewise linear differential systems defined on two sectors.
Preprint. November, 2016.
 [Abstract]

C. A. Buzzi, J. Llibre, R. A. T. Santos.
Global dynamics of a class of May-Leonard Lotka-Volterra systems.
Preprint. November, 2016.
 [Abstract]

J. Ginoux, J. Llibre.
On the Takens-Argémi-Benoît's transformation for the existence of canards solutions.
Preprint. October, 2016.
 [Abstract]

J. Llibre, C. Valls.
Polynomial, rational and analytic first integrals for an asymmetric family of 3-dimensional Lotka-Volterra systems.
Preprint. October, 2016.
 [Abstract]

J. Llibre, M. Messias, A. C. Reinol.
Quadratic polynomial differential systems in $R^3$ having invariant planes with total multiplicity 9.
Preprint. October, 2016.
 [Abstract]

J. Llibre, R. D. S. Oliveira, C. A. B. Rodrigues.
Limit cycles for two classes of control piecewise linear differential systems.
Preprint. July, 2016.
 [Abstract]

F. E. Lembarki, J. Llibre.
Periodic orbits for the generalized Yang-Mills Hamiltonian system in dimension 6: II.
Preprint. April, 2016.
 [Abstract]

F. Braun, J. Llibre.
On the connection between global centers and global injectivity.
Preprint. March, 2016.
 [Abstract]

J. Llibre, P. Pedregal.
Hilbert's 16th problem. When differential systems meet variational principles.
Preprint. February, 2019.
 [Preprint] [Abstract]

W. Aziz, C. J. Christopher, J. Llibre, C. Pantazi.
Local analytic first integrals of three-dimensional Lotka-Volterra systems with 3:-1:2-resonance.
Preprint. April, 2014.
 [Abstract]

Ll. Alsedà, S. Costa.
Coexistence of uncountably many attracting sets for skew-products on the cylinder.
Preprint. September, 2011.
 [Preprint] [Abstract]