On the polynomial limit cycles of polynomial differential equations.

Israel J. Math., to appear.

A Chebyshev criterion for Abelian integrals.

Trans. Amer. Math. Soc., to appear.

I.A. García, H. Giacomini & M. Grau 

Generalized Hopf Bifurcation for Planar Vector Fields via the Inverse Integrating Factor 

J. Dyn. Differ. Equ. 23 (2011), 251-281. 

A New Approach to Center Conditions for Simple Analytic Monodromic Singularities

 J. Differential Equations 248 (2010) 363–380

First integrals and Darboux polynomials of natural polynomial Hamiltonian systems.

Phys. Lett. A. 374 (2010), 4746–4748.

Periodic solutions of the perturbed symmetric Euler top.

Topol. Methods Nonlinear Anal. 36 (2010), 91-100.

A survey on the inverse integrating factor

Qual. Theory Dyn. Syst. 9 (2010), 115-166.

Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces.

Physica D 239 (2010), 1665-1669.

Analytic Nilpotent Centers with Analytic First Integral.

Nonlinear Anal. 72 (2010),  3732-3738.

Periodic Solutions of Second-Order Differential Equations with Two-Dimensional Lie Point Symmetry Algebra.

Nonlinear Anal. Real World Appl. 11 (2010) 4128-4140.

A New Approach to Center Conditions for Simple Analytic Monodromic Singularities

 J. Differential Equations 248 (2010) 363–380

The inverse integrating factor and the Poincaré map

Trans. Amer. Math. Soc., 362 (2010), 3591-3612.

Bifurcation of critical periods from Pleshkan's isochrones

J. Lond. Math. Soc., (2) 81 (2010), 142-160.

Weierstrass integrability of differential equations

Appl. Math. Lett. 23 (2010), 5, 523-526.

J. Giné & S. Maza

Orbital linearization in the quadratic Lotka-Volterra systems around singular points via Lie symmetries.

J. Nonlinear Math. Phys. 16 (2009), 455--464.

The center problem via averaging method. 

J. Math. Annal. Appl. 351 (2009), 334–339.

On the cyclicity of weight-homogeneous centers.

J. Differential Equations 246 (2009), 3126–3135

A note on linear differential equations with periodic coefficients.

Nonlinear Anal., 71 (2009), 3197-3202.

On the origin of the inertia: the Modified Newtonian Dynamics theory

Chaos Solitons Fractals 41 (2009), no. 4, 1651--1660.

Linearizable planar differential systems via the inverse integrating factor 

J. Phys. A: Math. Theor. 41 (2008), 135-205.

On the stability of periodic orbits for differential systems in Rn.

Discrete Contin. Dyn. Syst. Ser. B 10 (2008), 495-509. 

On the multiplicity of the circumference in planar polynomial vector fields.

Fixed Point Theory 9 (2008), 105-137.

Linearization of Analytic Isochronous Centers from a Given Commutator.

J. Math. Anal. Appl. 339 (2008) 740-745.

Linearization of Smooth Planar Vector Fields around Singular Points via Commuting Flows

Commun. Pure Appl. Anal. 7 (2008) 1415-1426.

On the origin of the anomalous precession of Mercury's perihelion.

Chaos Solitons Fractals 38 (2008), 1004-1010.

On the origin of the deflection of light

Chaos Solitons Fractals 35 (2008), no. 1, 1-6.

The role of algebraic solutions in planar polynomial differential systems 

Math. Proc. Cambridge Philos. Soc. 143 (2007), 487-508.

A. Gasull, J. Giné & M. Grau

Multiplicity of limit cycles and analytic m-solutions for planar differential systems.

J. Differential Equations 240 (2007), 375-398.

Invariant algebraic curves for the cubic Liénard system with linear damping.
Bull. Sci. Math. 130 (2006), 428-441.

The Poincaré problem in the non-resonant case: an algebraic approach.

Differ. Geom. Dyn. Syst. 8 (2006), 54-68.

Existence of limit cycles for real quadratic differential systems with an invariant cubic.

Pacific J. Math. 223 (2006), 201-218.

Non-nested configuration of algebraic limit cycles in quadratic systems

J. Differential Equations 225 (2006), 513-527.

A necessary condition in the monodromy problem for analytic differential equations on the plane

J. Symbolic Comput. 41 (2006), 943-958.

Integrability of planar polynomial differential systems through linear differential equations

Rocky Mountain J. Math. 36 (2006), 457-486.

J. Giné & M. Grau

Linearizability and integrability of vector fields via commutation.

J. Math. Anal. Appl., 319 (2006), 326-332.

A note on: "Relaxation Oscillators with Exact Limit Cycles".

J. Math. Anal. Appl., 324 (2006), 739-745.

Coexistence of algebraic and non-algebraic limit cycles, explicitly given.

Nonlinearity, 19 (2006), 1939-1950.

J. Giné & M. Grau

Characterization of isochronous foci for planar analytic differential systems.

Proc. Roy. Soc. Edinburgh Sect. A, 135 (2005), 985-998.

I.A. García & D.S. Shafer

Integral invariants and limit sets of planar vector fields

J. Differential Equations 217 (2005), 363 - 376.

J. Chavarriga, I.A. García & J. Sorolla

Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in Family (I) of chinese classification

Chaos, Solitons & Fractals 24 (2005), no. 2, 491-499.

Generalized nonlinear superposition principles for polynomial planar vector fields

J. Lie Theory 15 (2005), no. 1, 89-104.

Lie symmetries of quasihomogeneous polynomial planar vector fields and certain perturbations

Acta Mathematica Sinica 21 (2005), no. 1, 185-192.

On the existence of polynomial inverse integrating factors in quadratic systems with limit cycles

Dynam. Contin. Discrete Impuls. Systems 12 (2005), no. 2, 151-174.

Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields.

Rocky Mountain J. Math. 35 (2005), no. 2, 501-515.

Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems.

Bull. Sci. Math., 129 (2005), 99--126.

On the stability of limit cycles for planar differemtial systems.

J. Differential Equations, 213 (2005), 368--388.

Non-algebraic invariant curves for polynomial planar vector fields.

Discrete Contin. Dyn. Syst., 10 (2004), 755–768

Coexistence of limit cycles and invariant algebraic curves on a Kukles system.

Nonlinear Anal., 59 (2004), 673--693.

Generalized cofactors and nonlinear superposition principles

Applied Math. Lett. 16 (2003), no. 7, 1137-1141.

On the integrability of quasihomogeneous and related planar vector fields.

International Journal of Bifurcation & Chaos, 13 (2003), 995–1002

Some criteria for the existence and uniqueness of limit cycles for quadratic vector fields.

J. Math. Anal. Appl., 282 (2003), 296–304

Darboux integrability and the inverse integrating factor.

J. Differential Equations, 194 (2003), 116–139

Isochronous foci for analytic differential systems

Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13 (2003), 1617-1623

Local analytic integrability for nilpotent centers

Ergodic Theory Dynam. Systems, 23 (2003), 417-428

Invariant algebraic curves linear in one variable for planar real quadratic systems.

Applied Math. & Comput., 138 (2003), 291-308

A family of non Darboux-integrable quadratic polynomial differential systems with algebraic solutions of arbitrarily high degree.

Appl. Math. Lett., 16 (2003), 833-837.

Some open problems related to 16b Hilbert problem.

Sci. Ser. A Math. Sci. (N.S.), 9 (2003), 1 - 26.

Isochronous centers of a linear system perturbed by fifth degree homogeneous polynomial.

Journal of Computational and Applied Mathematics, 126 (2000) 351-368.

Polynomial inverse integrating factor.

Annals of Differential equations, 16 (2000) 320-329.

Quadratic systems having third degree invariant algebraic curves.

Revue Romaine de Mathematiques Pures et Appliquées 45 (2000), 93-106.

On the Integrability of Two-Dimensional Flows.

Journal of Diferential Equations 157 (1999), 163-182.

An improvement of the Darboux Theorem for systems with a center.

Applied Mathematics Letters, 12 (1999), 85-89.

A class of reversible cubic systems with an isochronous center.

Computers & Mathematics with Applications, 38 (1999), 39-53.