Preprints:

J. Huang, J. Torregrosa, J. Villadelprat.   NEW 2020-05-22
On the number of limit cycles in generalized abel equations.
Preprint. May, 2020.
 [Abstract]

D. Rojas, P. J. Torres.   NEW 2020-05-21
Periodic bouncing solutions of the Lazer-Solimini equation with weak repulsive singularity.
Preprint. May, 2020.
 [Preprint] [Abstract]

D. Marín, J. Villadelprat.   NEW 2020-05-20
Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: general setting.
Preprint. May, 2020.
 [Preprint] [Abstract]

J. L. R. Bastos, C. A. Buzzi, J. Torregrosa.   NEW 2020-05-12
Factor reversible systems with applications to planar centers.
Preprint. May, 2020.
 [Abstract]

E. Freire, E. Ponce, J. Torregrosa, F. Torres.   NEW 2020-05-09
Limit cycles from a monodromic infinity in planar piecewise linear systems.
Preprint. May, 2020.
 [Abstract]

A. Caicedo, J. Llibre, C. Vidal.   NEW 2020-05-08
Polynomial and rational first integrals for non-autonomous polynomial hamiltonian systems.
Preprint. May, 2020.
 [Abstract]

M. E. Anacleto, J. Llibre, C. Valls, C. Vidal.   NEW 2020-04-27
Limit cycles of discontinuous piecewise differential systems formed by linear centers in R^2 and separated by two circles.
Preprint. April, 2020.
 [Abstract]

J. J. Jimenez Ruiz, J. Llibre, J. C. Medrado.   NEW 2020-04-27
On the crossing limit cycles for piecewise linear differential systems separated by a straight line and having symmetric equilibrium points.
Preprint. April, 2020.
 [Abstract]

R. Benterki, L. Damene, J. Llibre.   NEW 2020-04-27
The limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by irreducible cubic curves II.
Preprint. April, 2020.
 [Abstract]

I. Sánchez Sánchez, J. Torregrosa.   NEW 2020-04-15
New lower bounds of the number of critical periods in reversible centers.
Preprint. April, 2020.
 [Abstract]

T. Li, J. Llibre.   NEW 2020-04-15
On the 16-th Hilbert problem for discontinuous piecewise polynomial Hamiltonian systems.
Preprint. April, 2020.
 [Abstract]

A. Belfar, R. Benterki, J. Llibre.   NEW 2020-04-15
Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibrium points and separated by irreducible cubics.
Preprint. April, 2020.
 [Abstract]

Ll. Alsedà, M. Misiurewicz, R. A. Pérez.   NEW 2020-04-07
Flexibility of entropies for piecewise expanding unimodal maps.
Preprint. April, 2020.
 [Preprint] [Abstract]

B. Campos, J. Canela, A. Garijo, P. Vindel.   NEW 2020-04-07
Dynamics of a family of rational operators of arbitrary degree.
Preprint. April, 2020.
 [Preprint] [Abstract]

K. Banerjee, X. Buff, J. Canela, A. Epstein.   NEW 2020-04-07
Tips of tongues in the double standard family.
Preprint. April, 2020.
 [Preprint] [Abstract]

C. Cufí-Cabré, J. Llibre.   NEW 2020-04-07
Minimal sets of Lefschetz periods of the Morse-Smale diffeomorphisms on S^n and S^m x S^n.
Preprint. April, 2020.
 [Abstract]

J. Llibre, C. Valls.   NEW 2020-04-07
The Markus-Yamabe conjecture for discontinuous piecewise linear differential systems in $R^n$ separated by a conic x $R^{n-2}$.
Preprint. April, 2020.
 [Abstract]

J. Llibre, C. Pantazi.   NEW 2020-04-07
Qualitative study of a model with Rastall gravity.
Preprint. April, 2020.
 [Abstract]

J. Llibre, C. Pantazi.   NEW 2020-04-07
Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3.
Preprint. April, 2020.
 [Abstract]

H. He, J. Llibre, D. Xiao.   NEW 2020-04-07
Hamiltonian polynomial differential systems with global centers in R2.
Preprint. April, 2020.
 [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]

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

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]

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]

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. 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]

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

R. Benterki, J. Llibre.
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.
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.
Lower bounds for the local cyclicity of centers using high order developments and parallelization.
Preprint. January, 2020.
 [Preprint] [Abstract]

A. Gasull, C. Valls.
Discrete Melnikov functions.
Preprint. December, 2019.
 [Preprint] [Abstract]

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

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

J. Llibre, A. Sá.
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.
Crossing periodic orbits via first integrals.
Preprint. December, 2019.
 [Abstract]

R. Benterki, J. Llibre.
Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points.
To appear in Mathematics.
 [Preprint] [Abstract]

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

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

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

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

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

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

A. Bakhshalizadeh, J. Llibre.
Limit cycles of piecewise differential equations on the cylinder.
Preprint. October, 2019.
 [Abstract]

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

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

A. Bakhshalizadeh, J. Llibre.
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.
Quadratic planar differential systems with algebraic limit cycles via quadratic plane Cremona maps.
Preprint. September, 2019.
 [Abstract]

J. Llibre, C. Valls.
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.
Non-existence and uniqueness of limit cycles for a class of $3$-dimensional piecewise linear differential systems.
Preprint. September, 2019.
 [Abstract]

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

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

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

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

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

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

M. R. Cândido, C. Valls.
Zero-Hopf bifurcation in the general van der Pol-Duffing equation.
Preprint. June, 2019.
 [Preprint] [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.
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]

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]

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]

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]

J. Llibre, Y. P. Martinez Mancilla.
Dynamics of a competitive Lotka-Volterra systems in R^3.
Preprint. 2020.
 [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 $R^3$ having a Darboux invariant.
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]

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, A. Makhlouf.
Zero-Hopf periodic orbits for a Rössler 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]

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

T. Chen, J. Llibre.
Topological classification of some SD Hamiltonian systems.
Preprint. August, 2018.
 [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, Y. P. Martinez Mancilla, C. Vidal.
Algebraic and topological classification of homogeneous quartic vector fields in the plane.
Preprint. May, 2018.
 [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]

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.
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 $R^3$.
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]

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

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

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

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]

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]

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]