W. Cui, J. Llibre.   NEW 2026-06-02
The dynamics on the invariant spheres of some $3$-dimensional polynomial differential systems.
Preprint. June, 2026.
Abstract

Ll. Alsedà, A. Garijo, X. Jarque.   NEW 2026-05-27
Mersenne numbers and the doubling map.
Preprint. May, 2026.
PreprintAbstract

F. Becatti, J. Llibre.   NEW 2026-05-22
Limit cycles of continuous piecewise differential systems formed by two rigid systems separated by one straight line.
Preprint. May, 2026.
Abstract

S. R. Alva, J. Llibre, A. C. Mereu.   NEW 2026-05-22
On the second part of Hilbert's 16th problem for some classes of discontinuous piecewise differential systems separated by a circle.
Preprint. May, 2026.
Abstract

J. Llibre.   NEW 2026-05-15
Global asymptotic stability for the rigid polynomial differential systems of degree three.
Preprint. May, 2026.
Abstract

J. Itikawa, J. Llibre.   NEW 2026-05-15
New families of planar Hamiltonian systems having global centers.
Preprint. May, 2026.
Abstract

L. L. Silva, J. Llibre.   NEW 2026-05-15
The dynamics of a polynomial differential system in $\mathbb{{R}}^3$.
Preprint. May, 2026.
Abstract

N. Chachapoyas, J. Llibre, I. S. Meza Sarmiento, J. Vidarte.   NEW 2026-04-29
Limit cycles of continuous-discontinuous piecewise linear Hamiltonian systems in $\mathbb R^2$ separated by the curve $y=e^x$.
Preprint. April, 2026.
Abstract

J. Llibre, B. R. de Freitas.   NEW 2026-04-29
Global attractors in a class of cubic polynomial differential systems.
Preprint. April, 2026.
Abstract

G. Rondon, P. R. Silva, J. Llibre.   NEW 2026-04-29
Limit cycles in piecewise smooth systems with circular switching manifold.
Preprint. April, 2026.
Abstract

J. Llibre, C. Valls.   NEW 2026-04-29
Three-dimensional Hopf bifurcation via averaging theory. Application to a virus vital model.
Preprint. April, 2026.
Abstract

J. Ginoux, R. Meucci, J. Llibre, G. Chen, L. O. Chua.   NEW 2026-04-23
Chaos via intermittency into generalized controlled nonlinear oscillators.
Preprint. April, 2026.
Abstract

T. Mayayo, J. Sardanyés, J. Torregrosa.   NEW 2026-04-17
Global dynamics and regime shifts in a resource-consumer model with facilitation and habitat loss.
Preprint. April, 2026.
Abstract

J. C. Artés, M. C. Mota, A. C. Rezende.   NEW 2026-04-07
Topological study of families with two infinite saddle-nodes of different types or with an infinite nilpotent singularity.
Preprint. April, 2026.
Abstract

J. C. Artés, J. Llibre, D. Schlomiuk, N. Vulpe.   NEW 2026-04-07
Codimension in planar polynomial differential systems.
Preprint. April, 2026.
Abstract

J. C. Artés, L. Cairó.   NEW 2026-04-07
Phase portraits of quadratic differential systems with a weak focus and a $\binom11 SN$.
Preprint. April, 2026.
Abstract

F. Becatti, B. R. de Freitas, J. Llibre.   NEW 2026-04-07
Limit cycles of continuous-discontinuous piecewise linear differential systems separated by one straight line.
Preprint. April, 2026.
Abstract

W. Cui, J. Llibre.   NEW 2026-04-07
Dynamics at infinity and on invariant algebraic surfaces of a generalized Lorenz-Type system.
Preprint. April, 2026.
Abstract

M. E. Anacleto, J. Llibre.   NEW 2026-03-27
Bifurcation of limit cycles from a cubic cente.
Preprint. March, 2026.
Abstract

V. Mañosa, C. Pantazi.   NEW 2026-03-24
Dynamics of Kahan-Hirota-Kimura maps with rational invariant fibrations.
Preprint. March, 2026.
PreprintAbstract

D. Juher, F. Mañosas, D. Rojas.   NEW 2026-03-23
Zero entropy cycles on trees: from Topology to Combinatorics and an application to star maps.
Preprint. March, 2026.
PreprintAbstract

J. C. Artés, L. Cairó, J. Llibre.   NEW 2026-03-17
Phase portraits of the families V to X for the quadratic polynomial differential systems.
Preprint. March, 2026. To appear in Abstract and Applied Analysis
Full PDF

B. Espigulé, D. Juher.   NEW 2026-03-10
Finite capture and the closure of roots of restricted polynomials.
Preprint. March, 2026.
PreprintAbstract

M. T. A. Cabrera, G. Anacona Erazo, J. Llibre.   NEW 2026-03-08
Global phase portrait of the Chen-Ueta dynamical system with invariants sets.
March, 2026.
Abstract

J. Llibre, A. Murza.   NEW 2026-03-08
Flow-invariant curves in fixed-point subspaces.
Preprint. March, 2026.
Abstract

Y. Li, J. Llibre.   NEW 2026-03-02
Global dynamics of a class of Rayleigh-Liénard systems (I): The Saddle Case.
Preprint. March, 2026.
Abstract

I. A. García, J. Giné, V. Mañosa.   NEW 2026-02-25
Monodromic singularities of Brunella-Miari vector fields with two edges in the Newton diagram.
Preprint. February, 2026.
Abstract

J. Llibre, C. Valls.   NEW 2026-02-16
Global asymptotical stability on the generalized polynomial Liénard systems.
LliVal2026. February, 2026.
Abstract

C. A. Buzzi, Y. R. Carvalho.   NEW 2026-02-16
Local bifurcations in a class of piecewise-smooth Filippov systems with a nonregular switching curve via a nonlinear double regularization process.
Preprint. February, 2026.
PreprintAbstract

J. Llibre, T. Salhi.   NEW 2026-02-16
Limit cycles and phase portraits of rigid polynomial differential systems.
Preprint. February, 2026.
Abstract

F. Braun, M. N. Cassiano, J. Llibre, L. F. Mello.   NEW 2026-02-06
Jacobian pairs for planar analytic quadratic-like submersion functions.
Preprint. February, 2026.
Abstract

T. M. P. de Abreu, J. Llibre.   NEW 2026-02-06
Classification of global phase portraits for the brusselator system.
Preprint. February, 2026.
Abstract

J. Andrade, J. Llibre, Y. P. Martinez-Mancilla.   NEW 2026-02-06
Global dynamics of a modified Wei system.
Preprint. February, 2026.
Abstract

J. Llibre, R. O. Ramírez.
Maximally superintegrability of the Hamiltonian systems.
Preprint. January, 2026.
Abstract

G. Anacona Erazo, J. Llibre.
Global dynamics of the Sprott dynamical system Case A with linear antidamping.
Preprint. January, 2026.
Abstract

J. Llibre, L. F. Mello.
On the invariant sphere theorem with emphasis in the round sphere $S^n$.
Preprint. January, 2026. To appear in ABAKOS
Abstract

J. Llibre, R. O. Ramírez, V. Ramírez.
On the integrability of the geodesic flow on homogeneous surfaces.
Preprint. January, 2026.
Abstract

J. Llibre, L. L. Silva.
Periodic orbits in slow - fast piecewise linear hamiltonian systems.
Preprint. January, 2026.
Abstract

A. Bakhshalizadeh, J. Llibre.
Continuous linear and quadratic differential systems on the 2-dimensional torus.
Preprint. January, 2026.
Abstract

J. Llibre.
On the Abel differential equations and the polynomial differential systems.
Preprint. January, 2026.
Abstract

M. R. Cândido, J. Llibre, M. Messias, C. Valls.
Multiple invariant sets bifurcating from a zero-Hopf equilibrium.
Preprint. January, 2026.
Abstract

W. Cui, J. Llibre.
Dynamics of a predator-prey model with alternative prey and scaled harvesting efforts.
Preprint. January, 2026.
Abstract

J. D. Huancas, J. Llibre, C. Vidal.
Dynamics of the stretch-twist-fold system.
Preprint. January, 2026.
Abstract

L. F. Gonçalves, R. Euzébio, V. C. Fernandes, J. Llibre.
Limit cycles of piecewise smooth vector fields formed by rigid systems and linear centers.
Preprint. January, 2026.
Abstract

J. Llibre, N. Sadri, M. Mousavi.
Qualitative study of the multimolecular reaction systems.
Preprint. December, 2025.
Abstract

J. Llibre, Y. Tang, J. Yu, P. Zhou.
Global dynamics of quadratic and cubic planar quasi-homogeneous differential systems.
Preprint. December, 2025.
Abstract

J. Llibre, R. D. S. Oliveira, C. A. B. Rodrigues de Lima.
Invariant cubics and Darboux invariants for planar polynomial differential systems.
Preprint. December, 2025.
Abstract

R. A. Garcia, J. Llibre.
Limit cycles for horizontal and vertical principal foliations.
Preprint. December, 2025.
Abstract

A. Bakhshalizadeh, J. Llibre.
Limit cycles in planar discontinuous piecewise linear Hamiltonian systems with three equal sectors.
Preprint. December, 2025.
Abstract

J. Llibre, A. Makhlouf.
Periodic orbits of a galactic Hamiltonian system.
Preprint. November, 2025.
Abstract

S. Jana, J. Llibre.
$n$-dimensional Lotka-Volterra systems with a Darboux invariant.
Preprint. November, 2025.
Abstract

M. T. A. Cabrera, R. Cristiano, J. Llibre.
Phase portraits of a Lotka-Volterra model with discontinuous harvesting action.
Preprint. November, 2025.
Abstract

J. Llibre, R. O. Ramírez.
Inverse problems for the Stäckel mechanical systems.
Preprint. November, 2025.
Abstract

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

W. M. Batista, J. Llibre, D. J. Tonon.
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.
Hopf bifurcation of limit cycles surrounding a node.
Preprint. October, 2025.
Abstract

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

J. Llibre, L. F. Mello.
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.
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.
Periodic orbits of hamiltonian systems in $R^{2n}$ via averaging theory.
Preprint. September, 2025.
Abstract

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

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

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

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

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

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, 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

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

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

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

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

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

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

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