Preprints:

J. Llibre, V. F. Sirvent.   NEW 2020-10-21
Periodic structure of the transversal maps on surfaces.
Preprint. October, 2020.
 [Abstract]

J. Llibre, Y. P. Martinez Mancilla, C. Vidal.   NEW 2020-10-21
Limit cycles of a perturbation of a polynomial Hamiltonian systems of degree 4 symmetric with respect to the origin.
Preprint. October, 2020.
 [Abstract]

O. A. R. Cespedes, J. Llibre.   NEW 2020-10-21
Zero-Hopf bifurcation in a modified van der pol-Duffing oscillator.
Preprint. October, 2020.
 [Abstract]

J. C. Artés, J. Llibre, D. Schlomiuk, N. Vulpe.   NEW 2020-10-21
Abel quadratic differential systems of second kind.
Preprint. October, 2020.
 [Abstract]

C. Cufí-Cabré, E. Fontich.   NEW 2020-10-06
Differentiable invariant manifolds of nilpotent parabolic points.
Preprint. October, 2020.
 [Preprint] [Abstract]

J. Llibre, C. Valls.   NEW 2020-09-23
Phase portraits of the complex Riccati equation with constant coefficients.
Preprint. September, 2020.
 [Abstract]

J. Llibre, C. Valls.   NEW 2020-09-21
The improved Euler-Jacobi formula and the planar cubic polynomial vector fields in $R^2$.
Preprint. September, 2020.
 [Abstract]

M. R. A. Gouveia, J. Llibre, L. A. Roberto.   NEW 2020-09-21
Phase portraits of a family of Hamiltonian cubic systems.
Preprint. September, 2020.
 [Abstract]

C. A. Buzzi, Y. R. Carvalho, A. Gasull.   NEW 2020-08-18
Limit cycles for some families of smooth and non-smooth planar systems.
Preprint. August, 2020.
 [Preprint] [Abstract]

J. Llibre, B. D. Lopes, P. R. Silva.   NEW 2020-08-17
Phase portraits of the Riccati quadratic polynomial differential system.
Preprint. August, 2020.
 [Preprint] [Abstract]

A. A. Rabia, J. Llibre, A. Makhlouf.   NEW 2020-08-11
Periodic solutions for two classes of Duffing differential equations via averaging theory.
Preprint. August, 2020.
 [Abstract]

C. A. Buzzi, Y. R. Carvalho, A. Gasull.   NEW 2020-08-07
The local period function for Hamiltonian systems with applications.
Preprint. August, 2020.
 [Preprint] [Abstract]

T. Li, J. Llibre.   NEW 2020-07-30
Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems.
Preprint. July, 2020.
 [Abstract]

J. Llibre, T. Saeed, E. E. Zotos.   NEW 2020-07-30
Periodic orbits and equilibria for a seventh-order generalized Hénon-Heiles Hamiltonian system.
Preprint. July, 2020.
 [Abstract]

J. Llibre, Y. Tian.   NEW 2020-07-30
The zero-Hopf bifurcations of a four-dimensional hyperchaotic system.
Preprint. July, 2020.
 [Abstract]

J. Llibre, O. Ramírez.   NEW 2020-07-30
Polynomial differential systems with invariant algebraic curves of arbitrarily high degree.
Preprint. July, 2020.
 [Abstract]

M. Esteban, J. Llibre, C. Valls.   NEW 2020-07-30
The 16th Hilbert problem for discontinuous piecewise isochronous centers of degree one or two separated by a straight line.
Preprint. July, 2020.
 [Abstract]

T. Li, J. Llibre.   NEW 2020-07-30
Limit cycles of piecewise polynomial differential systems with the discontinuity line xy=0.
Preprint. July, 2020.
 [Abstract]

J. Llibre, C. Valls.   NEW 2020-07-30
Twin quadratic polynomial vector fields in the space $C^3$.
Preprint. July, 2020.
 [Abstract]

R. Benterki, J. Llibre.   NEW 2020-07-27
Zero-Hopf bifurcation in a malaria model.
Preprint. July, 2020.
 [Abstract]

J. Llibre, C. Valls.   NEW 2020-07-27
Twin polynomial vector fields of arbitrary degree.
Preprint. July, 2020.
 [Abstract]

B. García, J. Llibre, A. Lombardero, J. S. Pérez del Río.   NEW 2020-07-27
Analytic integrability of quasi-homogeneous systems via the Yoshida method.
Preprint. July, 2020.
 [Abstract]

T. Li, J. Llibre.   NEW 2020-07-27
Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary.
Preprint. July, 2020.
 [Abstract]

J. Llibre, R. O. Ramírez, V. Ramírez.   NEW 2020-07-27
The center problem for the class of $\lambda$-$\Omega$ differential systems.
Preprint. July, 2020.
 [Abstract]

A. Gasull, H. Giacomini.   NEW 2020-06-29
Solving polynomials with ordinary differential equations.
Preprint. June, 2020.
 [Preprint] [Abstract]

T. Carvalho, L. F. Gonçalves, J. Llibre.   NEW 2020-06-29
Limit cycles on piecewise smooth vector fields with coupled rigid centers.
Preprint. June, 2020.
 [Abstract]

E. Diz Pita, J. Llibre, M. V. Otero Espinar, C. Valls.   NEW 2020-06-29
The zero-Hopf bifurcations in the Kolmogorov systems of degree 3 in $R^3$.
Preprint. June, 2020.
 [Abstract]

J. Llibre, V. F. Sirvent.
Entropy and periods for continuous graph maps.
Preprint. June, 2020.
 [Abstract]

F. Gao, J. Llibre.
Global dynamics of the Horava-Lifshitz cosmological model in a non-flat universe with non-zero cosmological constant.
Preprint. June, 2020.
 [Abstract]

A. M. Benini, V. Evdoridou, N. Fagella, P. J. Rippon, G. M. Stallard.
Classifying simply connected wandering domains.
Preprint. June, 2020.
 [Preprint] [Abstract]

J. Giné, J. Llibre.
A new sufficient condition in order that the real Jacobian conjecture in $R^2$ holds.
Preprint. June, 2020.
 [Abstract]

L. Gardini, A. Garijo, X. Jarque.
Topological properties of the immediate basins of attraction for the secant method.
Preprint. June, 2020.
 [Preprint] [Abstract]

J. Llibre, Y. Tian.
Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces.
Preprint. June, 2020.
 [Abstract]

E. Diz Pita, J. Llibre, M. V. Otero Espinar.
Phase portraits of a family of Kolmogorov systems depending on six parameters.
Preprint. June, 2020.
 [Abstract]

C. A. Buzzi, J. Llibre, P. Santana.
Phase portraits of (2;0) reversible vector fields with symmetrical singularities.
Preprint. June, 2020.
 [Abstract]

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

D. Marín, J. Villadelprat.
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.
Factor reversible systems with applications to planar centers.
Preprint. May, 2020.
 [Abstract]

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

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

M. E. Anacleto, J. Llibre, C. Valls, C. Vidal.
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.
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.
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 lower bounds of the number of critical periods in reversible centers.
Preprint. April, 2020.
 [Abstract]

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

A. Belfar, R. Benterki, J. Llibre.
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.
Flexibility of entropies for piecewise expanding unimodal maps.
Preprint. April, 2020.
 [Preprint] [Abstract]

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

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

C. Cufí-Cabré, J. Llibre.
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.
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.
Qualitative study of a model with Rastall gravity.
Preprint. April, 2020.
 [Abstract]

J. Llibre, C. Pantazi.
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.
Hamiltonian polynomial differential systems with global centers in $R^2$.
Preprint. April, 2020.
 [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, 2020.
 [Abstract]

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

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

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

J. Itikawa, J. Llibre.
New families of planar Hamiltonian systems having global centers.
Preprint. March, 2020.
 [Abstract]

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

J. Llibre, A. Murza, A. E. Teruel.
First integrals of a class of n-dimensional Lotka-Volterra differential systems.
Preprint. March, 2020.
 [Abstract]

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

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

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

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

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

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

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

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

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

J. Llibre, P. Pedregal.
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]

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]

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]

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]

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]

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, 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]

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 $R^2$.
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]

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]

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]

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

F. Braun, J. Llibre.
On the connection between global centers and global injectivity.
Preprint. June, 2017.
 [Abstract]

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

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