Preprints

T. Chen, S. Li, J. Llibre.   NEW 2021-04-15
Nilpotent bi-center in continuous piecewise $Z_2$-equivariant cubic polynomial Hamiltonian systems (I).
Preprint. 2021.
 [Abstract]

Z. Diab, J. L. G. Guirao, J. Llibre, A. Makhlouf.   NEW 2021-04-15
Limit cycles of a generalized Mathieu differential system.
Preprint. April, 2021.
 [Abstract]

J. Llibre, C. Valls.   NEW 2021-04-15
Dynamics of the szekeres system.
Preprint. April, 2021.
 [Abstract]

R. D. S. Oliveira, I. Sánchez Sánchez, J. Torregrosa.   NEW 2021-04-14
Simultaneous bifurcation of limit cycles and critical periods.
Preprint. April, 2021.
 [Abstract]

J. Itikawa, R. D. S. Oliveira, J. Torregrosa.   NEW 2021-04-09
First-order perturbation for multi-parameter center families.
Preprint. April, 2021.
 [Abstract]

J. L. R. Bastos, C. A. Buzzi, J. Torregrosa.   NEW 2021-03-29
Orbitally symmetric systems with applications to planar centers.
Preprint. March, 2021.
 [Abstract]

D. d. C. Braga, J. Llibre, L. F. Mello.   NEW 2021-03-12
Transcritical bifurcation at infinity in planar piecewise polynomial differential systems with two zones.
Preprint. March, 2021.
 [Preprint] [Abstract]

A. Gasull, A. Geyer, V. Mañosa.   NEW 2021-03-12
Persistence of periodic traveling waves and Abelian integrals.
Preprint. March, 2021.
 [Preprint] [Abstract]

J. Llibre, C. Valls.   NEW 2021-03-12
Polynomial differential systems with even degree have no global centers.
Preprint. March, 2021.
 [Abstract]

J. Llibre.   NEW 2021-03-12
On the Abel differential equations and the polynomial differential systems.
Preprint. March, 2021.
 [Abstract]

I. Sánchez Sánchez, J. Torregrosa.   NEW 2021-02-24
Hopf bifurcation in 3-dimensional polynomial vector fields.
Preprint. February, 2021.
 [Abstract]

C. A. Buzzi, A. L. Rodero, J. Torregrosa.   NEW 2021-02-10
Centers and limit cycles of vector fields defined on invariant spheres.
Preprint. February, 2021.
 [Abstract]

J. Canela, X. Jarque, D. A. Paraschiv.   NEW 2021-01-31
Achievable connectivities of Fatou components for a family of singular perturbations.
Preprint. January, 2021.
 [Preprint] [Abstract]

D. Marín, M. Saavedra, J. Villadelprat.   NEW 2021-01-31
Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centers.
Preprint. January, 2021.
 [Preprint] [Abstract]

X. Chen, T. Li, J. Llibre.   NEW 2021-01-29
Melnikov functions of arbitrary order for piecewise smooth differential systems in $R^n$ and applications.
Preprint. January, 2021.
 [Abstract]

J. Llibre, C. Valls.   NEW 2021-01-25
Dynamics of a class of 3-dimensional Lotka-Volterra systems.
Preprint. January, 2021.
 [Abstract]

R. Benterki, J. Jimenez, J. Llibre.   NEW 2021-01-25
Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibria separated by reducible cubics.
Preprint. January, 2021.
 [Abstract]

J. Llibre, C. Valls.   NEW 2021-01-25
Polynomial differential systems with hyperbolic limit cycles.
Preprint. January, 2021.
 [Abstract]

J. Llibre, C. Valls.   NEW 2021-01-25
Polynomial differential systems with invariant algebraic curves of arbitrary degree formed by Legendre polynomials.
Preprint. January, 2021.
 [Abstract]

J. Ginoux, D. Lebiedz, J. Llibre.   NEW 2021-01-25
Flow curvature manifold and energy of generalized Liénard systems.
Preprint. January, 2021.
 [Abstract]

J. Llibre, C. Valls.   NEW 2021-01-25
On the distribution of the zeros of some polynomial maps $( P, Q, R): R^3 \to R^3$.
Preprint. January, 2021.
 [Abstract]

J. Llibre, C. Valls.   NEW 2021-01-25
On the distribution of the zeros of some polynomial maps $( P, Q): R^2 \to R^2$.
Preprint. January, 2021.
 [Abstract]

J. Llibre, C. Valls.   NEW 2021-01-18
Phase portraits of the complex Abel polynomial differential systems.
Preprint. January, 2021.
 [Abstract]

C. Cufí-Cabré, J. Llibre.   NEW 2021-01-14
Periods of the Morse-Smale diffeomorphisms on $S^n$ and $S^m \times S^n$ and $HP^n$.
Preprint. January, 2021.
 [Abstract]

J. Llibre, C. Valls.   NEW 2021-01-13
Periodic orbits for a generalized Hénon-Heiles Hamiltonian system with an additional singular gravitational term.
Preprint. January, 2021.
 [Abstract]

A. Gasull, H. Giacomini.   NEW 2021-01-13
Effectiveness of the Bendixon-Dulac theorem.
Preprint. January, 2021.
 [Preprint] [Abstract]

D. Marín, J. Villadelprat.   NEW 2020-12-23
Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: coefficient properties.
Preprint. December, 2020.
 [Preprint] [Abstract]

Ll. Alsedà, S. Borrós.
An algorithm to compute rotation numbers in the circle.
Preprint. December, 2020.
 [Preprint] [Abstract]

J. Llibre.
Central configurations of the circular restricted 4-body problem with three equal primaries in the collinear central configuration of the 3-body problem.
Preprint. December, 2020.
 [Abstract]

B. Ghermoul, J. Llibre, T. Salhi.
Limit cycles of continuous piecewise differential systems formed by linear and quadratic isochronous centers I.
Preprint. December, 2020.
 [Abstract]

C. A. Buzzi, J. Llibre, P. Santana.
Phase portraits of (2;1) reversible vector fields of low codimension.
Preprint. December, 2020.
 [Abstract]

J. Llibre, T. Salhi.
Phase portraits of a SIR epidemic model.
Preprint. November, 2020.
 [Abstract]

M. Esteban, J. Llibre, C. Valls.
The extended 16-th Hilbert problem for discontinuous piecewise linear centers separated by a non-regular line.
Preprint. 2020.
 [Abstract]

J. Llibre.
Limit cycles of planar continuous piecewise differential systems separated by a parabola and formed by an arbitrary linear and quadratic centers.
Preprint. October, 2020.
 [Abstract]

A. Ferragut, A. Gasull, X. Zhang.
Meromorphic first integrals of analytic diffeomorphisms.
Preprint. October, 2020.
 [Preprint] [Abstract]

A. Cima, A. Gasull, V. Mañosa, F. Mañosas.
Pointwise periodic maps with quantized first integrals.
Preprint. October, 2020.
 [Preprint] [Abstract]

A. Gasull, L. Hernández-Corbato, F. R. Ruiz del Portal.
Parrondo's paradox for homeomorphisms.
Preprint. October, 2020.
 [Preprint] [Abstract]

C. Liu, J. Llibre, R. O. Ramírez, V. Ramírez.
Solution of the center problem for a class polynomial differential systems.
Preprint. October, 2020.
 [Abstract]

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

J. Llibre, Y. P. Martinez Mancilla, C. Vidal.
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.
Zero-Hopf bifurcation in a modified van der pol-Duffing oscillator.
Preprint. October, 2020.
 [Abstract]

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

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

J. Llibre, C. Valls.
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.
Phase portraits of a family of Hamiltonian cubic systems.
Preprint. September, 2020.
 [Abstract]

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

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

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

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

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

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

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

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

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

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

T. Carvalho, L. F. Gonçalves, J. Llibre.
Limit cycles on piecewise smooth vector fields with coupled rigid centers.
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]

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]

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

I. Sánchez Sánchez, J. Torregrosa.
New lower bounds of the number of critical periods in reversible centers.
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]

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

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

J. Itikawa, J. Llibre.
New families of planar Hamiltonian systems having global centers.
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. Llibre, Y. Tian.
Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4.
Preprint. March, 2020.
 [Abstract]

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

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

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

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

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

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, 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]

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

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]