J. Torregrosa.   NEW 2024-06-27
Cubic planar vector fields with high local cyclicity.
Preprint. June, 2024.
Abstract

C. A. Buzzi, D. J. Tonon, J. Torregrosa.   NEW 2024-06-27
Limit cycles for a piecewise polynomial potential perturbation of a symmetric 8-loop Hamiltonian.
Preprint. June, 2024.
Abstract

V. Mañosa, C. Pantazi.   NEW 2024-06-17
Kahan-Hirota-Kimura maps preserving original cubic Hamiltonians.
Preprint. June, 2024.
PreprintAbstract

L. P. C. Cruz, A. C. Rezende, J. Torregrosa.   NEW 2024-06-13
Hybrid simultaneous bifurcation of limit cycles in planar piecewise quadratic differential systems.
Preprint. June, 2024.
PreprintAbstract

P. Maesschalck, J. Torregrosa.   NEW 2024-06-13
Limit cycles and critical periods with non-hyperbolic slow-fast systems.
Preprint. June, 2024.
Abstract

J. Llibre, R. Tian.   NEW 2024-05-24
Phase portraits of cubic polynomial Kolmogorov differential systems having a rational first integral of degree three.
Preprint. May, 2024.
Abstract

J. Escobar A., L. Jiménez-Lara, J. Llibre.   NEW 2024-05-23
Two-center problem with harmonic-like interactions: periodic orbits and integrability.
Preprint. May, 2024.
Abstract

M. F. S. Lima, J. Llibre.   NEW 2024-05-12
The easiest polynomial differential system in $\mathbb{{R}}^3$ having an invariant elliptic paraboloid.
Preprint. May, 2024.
Abstract

A. C. Rezende, M. A. S. Santos, J. Torregrosa.   NEW 2024-05-12
Period function of planar reversible quadratic systems.
Preprint. May, 2024.
Abstract

A. Gasull, P. Santana.   NEW 2024-05-08
On a variant of Hilbert's 16th problem.
Preprint. May, 2024.
PreprintAbstract

J. Llibre, B. R. de Freitas.   NEW 2024-05-08
On the limit cycles bifurcating from the periodic orbits of the hamiltonian system with Hamiltonian $H=(x^{2n}+y^{2n})/(2n)$.
Preprint. May, 2024.
Abstract

J. Llibre, J. R. Moraes.   NEW 2024-04-30
Analytic study of two limit cycles bifurcating from a zero-Hopf equilibrium.
Preprint. April, 2024.
Abstract

M. J. Álvarez, B. Coll, A. Gasull, R. Prohens.   NEW 2024-04-22
More limit cycles for complex differential equations with three monomials.
Preprint. April, 2024.
PreprintAbstract

J. Llibre, C. Valls.   NEW 2024-04-22
On the dynamics of a hyperjek memristive system.
Preprint. April, 2024.
Abstract

A. C. Rezende, M. A. S. Santos, J. Torregrosa.   NEW 2024-04-20
Period function for a family of piecewise planar Hamiltonian systems.
Preprint. April, 2024.
Abstract

A. Gasull.   NEW 2024-04-16
From Abel's differential equations to Hilbert's 16th problem.
Preprint. April, 2024.
PreprintAbstract

M. F. S. Lima, J. Llibre.   NEW 2024-04-11
Hopf bifurcation for a class of predator-prey system with small immigration.
Preprint. April, 2024.
Abstract

L. P. C. Cruz, J. Torregrosa, M. Berdugo, J. Sardanyés.   NEW 2024-04-05
Resource-consumer dynamics in drylands: Modeling the role of plant-plant facilitation-competition shifts with a piecewise system.
Preprint. April, 2024.
PreprintAbstract

J. Llibre, L. P. Serantola.   NEW 2024-04-02
The easiest polynomial differential systems in $\mathbb{{R}}^3$ having an invariant cylinder.
Preprint. April, 2024.
Abstract

V. Castellanos, J. Llibre.   NEW 2024-03-22
Persistence and zero-Hopf equilibrium in the tritrophic food chain model with Holling functional response.
Preprint. March, 2024.
Abstract

M. Álvarez-Ramírez, J. Llibre.   NEW 2024-03-17
Global phase portrait of a rolling motion of ships equation.
Preprint. March, 2024.
Abstract

D. d. C. Braga, F. S. Dias, J. Llibre, L. F. Mello.   NEW 2024-03-10
The matching of two Markus-Yamabe piecewise smooth systems in the plane.
Preprint. March, 2024.
Abstract

D. Marín, J. Villadelprat.   NEW 2024-03-07
The cyclicity of hyperbolic hemicycles.
Preprint. March, 2024.
PreprintAbstract

J. C. Artés, C. Trullàs.   NEW 2024-03-07
Quadratic differential systems with a weak focus of first order and a finite saddle-node.
Preprint. March, 2024.
PreprintAbstract

J. C. Artés, M. C. Mota, A. C. Rezende.   NEW 2024-03-07
Quadratic differential systems with a finite saddle-node and an infinite saddle-node (1,1) SN - (B).
Preprint. March, 2024.
PreprintAbstract

J. C. Artés, M. C. Mota, A. C. Rezende.   NEW 2024-03-07
Quadratic differential systems with a finite saddle-node and an infinite saddle-node (1,1) SN - (A).
Preprint. March, 2024.
PreprintAbstract

V. Castellanos, J. Llibre.   NEW 2024-03-07
The transition between two ecological limit cycles in one predator-two competitive prey mode.
Preprint. March, 2024.
Abstract

C. A. Buzzi, A. L. Rodero, J. Torregrosa.
3−dimensional piecewise linear and quadratic vector fields with invariant spheres.
Preprint. March, 2024.
PreprintAbstract

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

I. A. García, J. Giné, J. Llibre.
Characterization of global centers by the monodromy at infinity.
Preprint. January, 2024.
Abstract

G. Dong, J. Llibre.
The uniform isochronous centers with homogeneous nonlinearities of degree 5.
Preprint. January, 2024.
Abstract

G. Dong, J. Llibre.
Periodic orbits for an autonomous version of the Duffing-Holmes oscillator.
Preprint. January, 2024.
Abstract

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

D. He, J. Llibre.
Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular discontinuous boundary (II).
Preprint. December, 2023.
Abstract

D. He, J. Llibre.
Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular discontinuous boundary (I).
Preprint. December, 2023.
Abstract

J. Llibre, R. Tian.
Periodic orbits and non-existence of $C^1$ first integrals for analytic differential systems exhibiting a zero-Hopf bifurcation in ${\mathbb {R}}^4$.
Preprint. December, 2023.
Abstract

M. Corbera, C. Valls.
Global nilpotent reversible centers with cubic nonlinearities symmetric with respect to the $y$-axis.
Preprint. December, 2023.
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, F. Braun.
Parallel vector fields and global injectivity in two dimensions.
Preprint. November, 2023.
Abstract

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, L. P. Serantola.
New families of global cubic centers.
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

D. Juher, F. Mañosas, D. Rojas.
Characterization of the tree cycles with minimum positive entropy for any period.
Preprint. October, 2023.
PreprintAbstract

J. Llibre, G. Rondon.
Global centers of a class of cubic polynomial differential systems.
Preprint. October, 2023.
Abstract

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

C. Cufí-Cabré, E. Fontich.
Invariant manifolds of maps and vector fields with nilpotent parabolic tori.
Preprint. October, 2023.
PreprintAbstract

J. Llibre, T. Salhi.
Periodic orbits of continuous-discontinuous piecewise differential systems with four pieces separated by the curve $xy=0$ and formed by linear Hamiltonian systems.
Preprint. October, 2023.
Abstract

J. Llibre, Y. Zhao, S. Li.
On the index of an isolated equilibrium point for piecewise polynomial differential systems.
Preprint. October, 2023.
Abstract

J. Llibre, X. Sun.
Small-amplitude periodic solutions in the jerk equation of arbitrary degree.
Preprint. October, 2023.
Abstract

J. Llibre, C. Valls.
The dynamics of the Ladder system.
Preprint. September, 2023.
Abstract

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

S. Hussein, J. Llibre.
On the integrability of a Sprott cubic conservative jerk system.
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

R. F. Appis, J. Llibre.
Global centers of a family of cubic systems.
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, C. Valls.
Global asymptotic stability in quadratic systems.
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

V. Castellanos, J. Llibre.
Zero-Hopf bifurcation in a family of tritrophic food chain model with Holling III-III functional response.
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. Li, J. Llibre.
Continuous-discontinuous piecewise differential systems with two pieces separated by a non-regular line.
Preprint. April, 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

B. Ghermoul, J. Llibre.
Limit cycles for a class of continuous-discontinuous piecewise differential systems.
Preprint. April, 2023.
Abstract

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

L. Barreira, J. Llibre, C. Valls.
Flows with constant slope on the Klein bottle.
Preprint. March, 2023.
Abstract

D. d. C. Braga, F. S. Dias, J. Llibre, L. F. Mello.
The discontinuous matching of two globally asymptotically stable crossing piecewise smooth systems in the plane do not produce in general a piecewise differential system globally asymptotically stable.
Preprint. February, 2023.
Abstract

Y. Bao, S. Li, J. Llibre, Y. Zhao.
On the number of limit cycles for two classes of polynomial differential systems.
Preprint. January, 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

J. Li, J. Llibre.
The global dynamics of the Painlevé-Gambier equations XVIII, XXI and XXII.
Preprint. November, 2022.
Abstract

J. Ginoux, J. Llibre.
Zero-Hopf bifurcation in the Chua's circuit.
Preprint. November, 2022.
Abstract

J. Casimiro, J. Llibre.
Limit cycles of continuous piecewise smooth differential systems.
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. Llibre, Y. Zhao.
Final evolutions for Lotka-Volterra systems in $R^3$ having a Darboux invariant.
Preprint. October, 2022.
Abstract

Z. Guo, J. Llibre.
Limit cycles bifurcating from a zero-Hopf equilibrium of the Lotka-Volterra systems in $R^n$.
Preprint. October, 2022.
Abstract

T. Chen, J. Llibre.
Topological classification of some SD Hamiltonian systems.
Preprint. August, 2022.
Abstract

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. Llibre, C. Valls.
The classical and improved Euler-Jacobi formula and polynomial vector fields in $R^n$.
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, Y. P. Martinez Mancilla.
Limit cycles bifurcating from Kolmogorov systems of degree 4 in $R^2$ and $R^3$.
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. E. Anacleto, J. Llibre, C. Valls, C. Vidal.
On the crossing limit cycles created by discontinuous piecewise differential system formed by three linear Hamiltonian saddles.
Preprint. February, 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. Giné, J. Llibre.
The solution of the Poincaré problem on the rational first integral for the Liénard polynomial differential equations.
Preprint. February, 2022.
Abstract

J. Llibre, C. Valls.
The extended 16-th 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.
Abstract

J. Llibre, C. Valls.
Phase portraits of the equation $\ddot x + a x \dot x + b x^3=0$.
Preprint. November, 2021.
Abstract

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

C. Bouaziz, J. Llibre, D. Djedid, A. Makhlouf.
Zero-Hopf bifurcations for a class of 3-dimensional Lotka-Volterra systems.
Preprint. October, 2021.
Abstract

J. Llibre, C. Valls.
The 16th Hilbert problem for discontinuous piecewise linear Hamiltonian saddles and isochronous centers of degree two separated by a straight line.
Preprint. June, 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

C. Liu, J. Llibre, R. O. Ramírez, V. Ramírez.
Solution of the center problem for a class polynomial differential systems.
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

M. R. A. Gouveia, J. Llibre, L. A. Roberto.
Phase portraits of a family of Hamiltonian cubic systems.
Preprint. September, 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