M. E. Anacleto, J. Llibre.   NEW 2026-10-01
Bifurcation of limit cycles from the cubic centers $\dot x= -yR(x,y)$, $\dot y= xR(x,y)$, being $R(x,y)=0$ one of the nine conics.
Preprint. October, 2026.
Abstract

J. Llibre, Y. Zhao.   NEW 2026-09-25
Periodic orbits of a piecewise hybrid relay system separated by a sphere in $\mathbb R^3$.
Preprint. September, 2026.
Abstract

M. T. A. Cabrera, G. Anacona Erazo, J. Llibre.   NEW 2026-09-18
Bounded homogeneous polynomial differential systems of degree 5.
Preprint. September, 2026.
Abstract

J. C. Artés, C. Bujac, D. Schlomiuk, N. Vulpe.   NEW 2026-09-18
Phase portraits of real quadratic differential systems possessing an invariant ellipse.
Preprint. September, 2026.
Abstract

J. Llibre, C. Valls.   NEW 2026-09-09
Dynamics of the Tolman-Oppenheimer-Volkoff equation.
Preprint. September, 2026.
Abstract

A. Bakhshalizadeh, J. Llibre.   NEW 2026-09-09
Global dynamics of quadratic differential systems in $R^3$ having an invariant torus.
Preprint. September, 2026.
Abstract

G. Anacona Erazo, B. R. Freitas, R. Huzak, D. Rojas.   NEW 2026-09-08
The period function in regularized piecewise smooth planar systems.
Preprint. 2026.
PreprintAbstract

W. Szuminski, J. Llibre.   NEW 2026-09-04
Dynamics, periodic orbits and $C^1$ non-integrability of the ABC flow.
Preprint. September, 2026.
Abstract

W. Cui, J. Llibre.   NEW 2026-08-15
Explicit expression of the Hopf periodic orbit in the Wang-Chen system.
Preprint. August, 2026.
Abstract

C. Cao, J. Llibre.   NEW 2026-08-15
Global attractors in a family of asymmetric cubic-quadratic differential systems.
Preprint. August, 2026.
Abstract

L. P. C. Cruz, R. D. S. Oliveira, B. de Carvalho.   NEW 2026-07-20
Simultaneous limit cycle bifurcations and phase portraits in double-Reversible cubic systems with a saddle at the origin.
Preprint. July, 2026.
PreprintAbstract

G. Anacona Erazo, J. Llibre, B. R. Freitas.   NEW 2026-07-09
Lower bounds on the number of limit cycles for a class of Hamiltonian systems.
Preprint. July, 2026.
Abstract

J. Llibre, W. Szuminski.   NEW 2026-07-03
Zero-Hopf bifurcation, periodic orbits and $C^1$ non-integrability of the classical Rössler system.
Preprint. July, 2026.
Abstract

A. M. Escobar, L. Jiménez-Lara, J. Llibre.   NEW 2026-06-30
Global phase portrait of the planar Smorodinsky-Winternitz system.
Preprint. June, 2026.
Abstract

Y. Dai, J. Llibre.   NEW 2026-06-16
Global phase portraits and limit cycles of a Leslie-Gower model with Beddington-DeAngelis functional response.
Preprint. June, 2026.
Abstract

J. C. Artés, J. Llibre, D. Schlomiuk, N. Vulpe.   NEW 2026-06-16
Phase portraits of a family of real quadratic differential systems possessing a nilpotent or intricate singularity at infinity.
Preprint. June, 2026.
Abstract

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

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

F. Becatti, J. Llibre.
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.
On the second part of Hilbert's 16th problem for some classes of discontinuous piecewise differential systems separated by a circle.
Preprint. May, 2026.  [MR]
Abstract

L. P. C. Cruz, R. D. S. Oliveira, A. L. Rodero.
Center and cyclicity problems in a class of planar piecewise smooth vector fields with four zones.
Preprint. May, 2026.
PreprintAbstract

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

L. L. Silva, J. Llibre.
The dynamics of a polynomial differential system in $R^3$.
Preprint. May, 2026.
Abstract

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

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

J. Llibre, C. Valls.
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.
Chaos via intermittency into generalized controlled nonlinear oscillators.
Preprint. April, 2026.
Abstract

T. Mayayo, J. Sardanyés, J. Torregrosa.
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.
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, L. Cairó.
Phase portraits of quadratic differential systems with a weak focus and a $\binom11 SN$.
Preprint. April, 2026.
Abstract

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

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

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

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

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

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

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

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

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

C. A. Buzzi, Y. R. Carvalho.
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.
Limit cycles and phase portraits of rigid polynomial differential systems.
Preprint. February, 2026.
Abstract

J. Andrade, J. Llibre, Y. P. Martinez-Mancilla.
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

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

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

J. Llibre, A. Makhlouf.
Periodic orbits of a galactic Hamiltonian system.
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, B. D. Lopes, J. R. Moraes.
On the limit cycles of a class of cubic polynomial differential systems.
Preprint. October, 2025.
Abstract

J. Giné, M. Grau, J. Llibre.
Hopf bifurcation of limit cycles surrounding a node.
Preprint. October, 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

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

B. R. 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

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. 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

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

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

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

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