J. Llibre, B. D. Lopes, J. R. Moraes.   NEW 2025-10-29
On the limit cycles of a class of cubic polynomial differential systems.
Preprint. October, 2025.
Abstract

E. Diz Pita, J. Llibre, M. V. Otero Espinar, C. Valls.   NEW 2025-10-27
On the dynamics of the autonomous Duffing-Holmes oscillator.
Preprint. October, 2025.
Abstract

W. M. Batista, J. Llibre, D. J. Tonon.   NEW 2025-10-19
Sewing limit cycles for piecewise smooth systems with two linear centers and a coupled rigid center.
Preprint. October, 2025.
Abstract

J. Giné, M. Grau, J. Llibre.   NEW 2025-10-19
Hopf bifurcation of limit cycles surrounding a node.
Preprint. October, 2025.
Abstract

A. Gasull, P. Santana.   NEW 2025-10-13
Limit cycles and invariant algebraic curves.
Preprint. October, 2025.
PreprintAbstract

J. Llibre, L. F. Mello.   NEW 2025-10-13
The global injectivity of $C^2$ maps in $R^2$.
Preprint. October, 2025.
Abstract

J. Llibre, L. F. Mello.   NEW 2025-10-10
A necessary and sufficient condition and some sufficient conditions in order that the real Jacobian conjecture in $R^2$ holds.
Preprint. October, 2025.
Abstract

B. Muthuswamy, J. Ginoux, R. Meucci, J. Llibre, L. O. Chua.   NEW 2025-09-26
Reverse newhouse-Ruelle-Takens route to chaos and time-Dependent hamiltonian formulation of a generalized muthuswamy-Chua system.
Preprint. September, 2025.
Abstract

X. Hu, B. Huang, J. Llibre, Y. Tang.   NEW 2025-09-17
Periodic orbits of hamiltonian systems in $R^{2n}$ via averaging theory.
Preprint. September, 2025.
Abstract

A. Gasull, D. D. Novaes, J. Torregrosa.   NEW 2025-09-04
Weak-Coppel problem for a class of Riccati differential equations.
Preprint. September, 2025.
PreprintAbstract

A. Murza, J. Llibre.   NEW 2025-08-20
Darboux theory of integrability for real polynomial vector fields on the n-dimensional hyperboloid.
Preprint. August, 2025.
Abstract

Y. Li, J. Llibre.   NEW 2025-08-20
Dynamics of a differential system in $R^3$ with a simple chaotic flow.
Preprint. August, 2025.
Abstract

J. Llibre, A. Murza.   NEW 2025-08-11
Invariant meridians and parallels on the hyperboloid of one sheet.
Preprint. August, 2025.
Abstract

J. Llibre, H. Zeng.
Global phase portraits of a SIS model with importation and removal.
Preprint. July, 2025.
Abstract

Á. Fernández-Mora, À. Haro, J. M. Mondelo.
On the convergence of flow map parametrization methods in Hamiltonian systems.
Preprint. June, 2025.
PreprintAbstract

L. Queiroz, J. Llibre.
On a class of Hamiltonian Kolmogorov systems.
Preprint. June, 2025.
Abstract

R. F. Appis, J. Llibre.
No global centers in a class of cubic systems.
Preprint. June, 2025.
Abstract

J. Llibre, A. C. Rezende, L. P. Serantola.
The periodic orbits of some classes of $3$-dimensional relay hybrid systems.
Preprint. June, 2025.
Abstract

J. Llibre, A. C. T. Sánchez, D. J. Tonon.
Limit cycles of discontinuous piecewise hybrid rigid systems separated by a straight line.
Preprint. June, 2025.
Abstract

A. Murza, J. Llibre.
Polynomial vector fields on the whitney umbrella.
Preprint. June, 2025.
Abstract

J. Llibre, G. Rondon.
The dynamics of the Ehrhard-Müller system with invariant algebraic surfaces.
Preprint. May, 2025.
PreprintAbstract

R. D. S. Oliveira, A. L. Rodero, J. Torregrosa.
Mixed simultaneous cyclicity for piecewise smooth vector fields defined on an invariant sphere.
Preprint. May, 2025.
Abstract

D. Marín, J. Villadelprat.
Derivatives of the separation function of generalized saddle connections.
Preprint. May, 2025.
PreprintAbstract

A. C. Rezende, M. A. S. Santos, J. Torregrosa.
The period function of centers at infinity in planar piecewise linear systems.
Preprint. May, 2025.
Abstract

M. Domingues, J. Llibre, L. F. Mello.
A new sufficient condition in order that the real Jacobian conjecture in $R^2$ holds.
Preprint. April, 2025.
Abstract

B. R. de Freitas, D. Avila, F. Becatti, J. Llibre.
Limit cycles of continuous-discontinuous piecewise differential systems formed by two Hamiltonian systems and separated by a non-regular line.
Preprint. April, 2025.
Abstract

X. Hu, B. Huang, J. Llibre, Y. Tang.
ZeroHopf and nilpotent zero-Hopf bifurcation of periodic orbits in Hamiltonian systems.
Preprint. April, 2025.
Abstract

J. C. Artés, L. Cairó, J. Llibre.
Phase portraits of the families VII and VIII of the quadratic polynomial differential systems.
Preprint. April, 2025.
Abstract

G. Rondon, P. R. Silva, L. F. d. S. Gouveia.
Holomorphic slow-fast systems.
Preprint. April, 2025.
PreprintAbstract

M. Garrido, P. Martín, J. Paradela.
Parabolic saddles and Newhouse domains in celestial mechanics.
Preprint. April, 2025.
PreprintAbstract

M. E. Anacleto, J. Llibre, C. Valls.
Global dynamics of the predator-prey Rosenzweig-MacArthur model with Allee effect.
Preprint. March, 2025.
Abstract

J. Llibre, Y. P. Martinez-Mancilla.
On the Hamiltonian Hopf bifurcation in the 3D Hénon-Heiles Hamiltonian revised.
Preprint. March, 2025.
Abstract

J. Llibre, Y. P. Martinez-Mancilla.
Hopf bifurcation in kolmogorov systems of degree of degree 4 in $R^2$ and $R^3$.
Preprint. March, 2025.
Abstract

A. Cima, A. Gasull, V. Mañosa, F. Mañosas.
Further results for a family of continuous piecewise linear planar maps.
Preprint. February, 2025.
PreprintAbstract

T. Chen, J. Llibre, H. Zhang.
Dynamics for a Rayleigh-Liénard-Duffing oscillator in wing rock.
Preprint. February, 2025.
Abstract

A. C. Fernandes, J. Llibre, L. F. Mello, A. M. Silva.
The symmetries in the spatial (1+5)-body problem.
Preprint. February, 2025.
Abstract

J. Llibre, H. Zeng.
Limit cycles of planar discontinuous piecewise linear Hamiltonian systems separated by irreducible cubic curves.
Preprint. February, 2025.
Abstract

J. D. García Saldaña, A. Gasull, S. Rebollo-Perdomo.
A new family of integrable differential systems in arbitrary dimension.
Preprint. January, 2025.
PreprintAbstract

Y. Li, J. Llibre.
Rigid polynomial differential systems with quartic homogeneous nonlinearities.
Preprint. January, 2025.
Abstract

J. Llibre, T. Salhi.
New dynamics in the Rössler system.
Preprint. December, 2024.
Abstract

J. Li, J. Llibre.
On the limit cycles of two classes of discontinuous piecewise Hamiltonian differential systems.
Preprint. December, 2024.
Abstract

J. Llibre, R. D. S. Oliveira.
Limit cycles of planar discontinuous piecewise linear Hamiltonian systems in three regions of Y-type.
Preprint. November, 2024.
Abstract

J. Llibre, A. Murza.
Polynomial vector fields on the Möbius strip.
Preprint. November, 2024.
Abstract

J. Llibre, X. Zhang.
Zero-Hopf equilibria in Hamiltonian systems.
Preprint. October, 2024.
Abstract

G. Anacona Erazo, J. Llibre, B. R. de Freitas.
Centers of cubic polynomial differential equations.
Preprint. October, 2024.
Abstract

E. Diz Pita, J. Llibre, M. V. Otero Espinar, C. Valls.
On the integrability and dynamics of the Hide, Skeldon and Acheson differential system.
Preprint. October, 2024.
Abstract

Z. Guo, J. Llibre.
The dynamics of the planar Hindmarsh-Rose burster system.
Preprint. October, 2024.
Abstract

J. Llibre, C. A. B. Rodrigues.
On the limit cycles of piecewise hybrid Hamiltonian linear systems separated by a circle.
Preprint. October, 2024.
Abstract

J. Llibre, L. P. Serantola.
Hopf bifurcation for the prey-predator Rosenzweig-MacArthur model.
Preprint. September, 2024.
Abstract

J. Llibre, A. Murza.
Darboux theory of integrability for real polynomial vector fields on the $n-$dimensional ellipsoid.
Preprint. September, 2024.
Abstract

M. R. A. Gouveia, J. Llibre, L. A. Roberto.
Periodic orbits in a perturbed Henon-Heiles Hamiltonian system.
Preprint. August, 2024.
Abstract

M. Belattar, J. Llibre.
The global dynamics of a Rayleigh system.
Preprint. August, 2024.
Abstract

J. C. Artés, J. Llibre, D. Schlomiuk, N. Vulpe.
Codimension in planar polynomial differential systems.
Preprint. August, 2024.
Abstract

J. Llibre, R. Tian.
The dynamics of a family of rigid polynomial differential systems of degree three.
Preprint. August, 2024.
Abstract

J. Llibre, A. Makhlouf.
The zero-Hopf bifurcations of the quadratic polynomial differential jerk systems in ${{R}^3}$.
Preprint. July, 2024.
Abstract

A. M. Escobar, L. Jiménez-Lara, J. Llibre.
Two-center problem with harmonic-like interactions: periodic orbits and integrability.
Preprint. May, 2024.
Abstract

M. F. S. Lima, J. Llibre.
The easiest polynomial differential system in ${{R}}^3$ having an invariant elliptic paraboloid.
Preprint. May, 2024.
Abstract

A. C. Rezende, M. A. S. Santos, J. Torregrosa.
Period function of planar reversible quadratic systems.
Preprint. May, 2024.
Abstract

J. C. Artés, C. Trullàs.
Quadratic differential systems with a weak focus of first order and a finite saddle-node.
Preprint. March, 2024.
PreprintAbstract

J. Llibre, R. Tian.
On the invariant straight lines of the polynomial differential systems in ${{R}}^3$.
Preprint. February, 2024.
Abstract

J. Llibre, R. Tian.
The easiest polynomial differential systems in ${{R}}^4$ having an invariant sphere.
Preprint. January, 2024.
Abstract

M. Corbera, C. Valls.
Phase portraits of a generalized Liénard system with homogeneous nonlinearities.
Preprint. December, 2023.
Abstract

W. Aziz, C. J. Christopher, C. Pantazi, S. Walcher.
Liouvillian integrability of three dimensional vector fields.
Preprint. December, 2023.
PreprintAbstract

J. Llibre, X. Zhang.
Periodic orbits and non-existence of $C^1$ first integrals for analytic differential systems exhibiting a zero-Hopf bifurcation in $R^3$.
Preprint. November, 2023.
Abstract

J. Llibre, J. Yu.
Periodic orbits and $C^1$ non-integrability of the 3D van der Pol-Duffing oscillator system.
Preprint. November, 2023.
Abstract

J. Llibre, C. Valls.
On the dynamics of the ACDM model of the universe.
Preprint. November, 2023.
Abstract

J. Llibre, L. Baymout, R. Benterki.
Bifurcation of limit cycles in a class of discontinuous piecewise differential systems.
Preprint. October, 2023.
Abstract

J. J. Jimenez Ruiz, J. Llibre.
Limit cycles for continuous and discontinuous perturbations of two cubic isochronous centers.
Preprint. August, 2023.
Abstract

A. A. Rabia, J. Llibre, A. Makhlouf.
Periodic solutions for two classes of Duffing differential equations via averaging theory.
Preprint. August, 2023.
Abstract

Z. Diab, J. L. G. Guirao, J. Llibre.
Periodic orbit in the zero-Hopf bifurcation of the 5-dimensional hyper-chaotic Lorenz system.
Preprint. July, 2023.
Abstract

J. J. Jimenez Ruiz, J. Llibre.
Limit cycles for a class of discontinuous piecewise differential systems in $R^3$ separated by a quadric.
Preprint. July, 2023.
Abstract

L. P. C. Cruz, J. Llibre.
Global centers in a class of quintic polynomial differential system.
Preprint. June, 2023.
Abstract

J. J. Jimenez Ruiz, J. Llibre.
Dynamics of the flows with constant slope on the cylinder and on the Möbius strip.
Preprint. June, 2023.
Abstract

R. Meucci, J. Llibre, E. Pugliese, J. Ginoux.
Dynamics of a two-level laser model with delay.
Preprint. June, 2023.
Abstract

J. Llibre, D. He.
Limit cycles from the perturbation of a quadratic uniform isochronous center inside the discontinuous piecewise quadratic polynomial differential systems.
Preprint. June, 2023.
Abstract

M. R. A. Gouveia, J. Llibre, L. P. Serantola.
Limit cycles of a class of discontinous piecewise differential systems.
Preprint. June, 2023.
Abstract

M. Duran Baldissera, B. de Carvalho, J. Llibre.
Phase portraits of completely symmetric centers.
Preprint. May, 2023.
Abstract

L. Barreira, J. Llibre, C. Valls.
A weakened Markus-Yamabe condition for generalized $\varphi$-Laplacian Liénard systems.
Preprint. May, 2023.
Abstract

J. Llibre.
Periodic orbits near an equilibrium for Hamiltonian systems with 2 degrees of freedom.
Preprint. April, 2023.
Abstract

Ll. Alsedà, D. Juher, J. Los, F. Mañosas.
Entropy stability and Milnor-Thurston invariants for Bowen-series-like maps.
Preprint. April, 2023.
PreprintAbstract

J. Llibre, D. Schlomiuk.
On the graphics in quadratic differential systems.
Preprint. April, 2023.
Abstract

L. Baymout, R. Benterki, J. Llibre.
On the maximum number of limit cycles of discontinuous piecewise differential systems formed by a cubic uniform isochronous center and a linear center separated by a straight line.
Preprint. November, 2022.
Abstract

A. Bakhshalizadeh, J. Llibre.
Continuous linear and quadratic differential systems on the 2-dimensional torus.
Preprint. November, 2022.
Abstract

Ll. Alsedà, S. Costa.
Coexistence of uncountably many attracting sets for skew-products on the cylinder.
Preprint. November, 2022.
PreprintAbstract

J. Li, J. Llibre.
Global dynamics of the Ermakov-Pinney equation.
Preprint. May, 2022.
Abstract

J. Llibre, R. O. Ramírez.
Generalization of the Laplace-Runge-Lenz conservation law.
Preprint. May, 2022.
Abstract

J. Li, J. Llibre.
Limit cycles of discontinuous piecewise differential systems separated by a straight line and formed by two cubic reversible isochronous centers.
Preprint. April, 2022.
Abstract

J. Li, J. Llibre.
On the limit cycles of the differential equations $dr/d\theta = a_n(\theta)r^n+a_{n-1}(\theta)r^{n-1}+\cdots+a_0(\theta)$.
Preprint. March, 2022.
Abstract

J. Li, J. Llibre.
Limit cycles of the piecewise differential systems.
Preprint. March, 2022.
Abstract

J. Llibre, J. R. Moraes.
Limit cycles of discontinuous piecewise differential systems in $R^2$ separated by one or two parallel straight lines and formed by arbitrary linear Hamiltonian systems.
Preprint. March, 2022.
Abstract

M. F. S. Lima, J. Llibre.
Double zero-Hopf bifurcation in a four-dimensional hyperchaotic system.
Preprint. February, 2022.
Abstract

C. A. Buzzi, A. L. Rodero, M. A. Teixeira.
Stability conditions for piecewise refractive vector fields partially integrable.
Preprint. February, 2022.
Abstract

J. Llibre, C. Valls.
The extended 16th Hilbert problem for piecewise linear systems separated by a non-regular line.
Preprint. January, 2022.
Abstract

J. C. Artés, J. Llibre, N. Vulpe.
Dynamics of the static star differential system from the mathematical and physical point of views.
Preprint. November, 2021.
PreprintAbstract

J. Llibre, R. O. Ramírez, V. Ramírez.
On the integrability of the geodesic flow on homogeneous surfaces.
Preprint. November, 2021.
Abstract

J. Llibre.
On the Abel differential equations and the polynomial differential systems.
Preprint. March, 2021.
Abstract

J. Llibre, C. Valls.
On the distribution of the zeros of some polynomial maps $( P, Q): R^2 \to R^2$.
Preprint. January, 2021.
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, O. Ramírez.
Polynomial differential systems with invariant algebraic curves of arbitrarily high degree.
Preprint. July, 2020.
Abstract

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

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

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

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

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.
Phase portraits and bifurcation diagrams for some Hamiltonian systems with rational potentials.
Preprint. June, 2018.
Abstract