My main interest is the understanding of the global behaviour of dynamical systems. I have been working on differential equations (autonomous or not) and on discrete dynamical systems, with special emphasis on difference equations. In my research, apart from the general theory of dynamical systems, I use techniques of analysis, geometry, algebra, algebraic geometry, numerical analysis and simulation.
I have published more than 100 papers collaborating with 45 researches around the world. Together with some of them I have solved several conjectures: the Markus-Yamabe Conjecture about global asymptotic stability of differential equations, open since 1960; the Composition Conjecture appearing in the study of Abel equations; and a conjecture of E. C. Zeeman about the existence of rational 9-periodic points for the Lyness recurrence. I also have contributed to the qualitative theory of planar differential equations, with my results on the number of limit cycles and the period function.
Recently, my joint paper, A. Cima, A. Gasull and V. Mañosas, Basin of attraction of triangular maps with applications, has received the prize to the best paper published in Journal of Difference Equations and its Applications during 2014.
- Dynamical systems
- Ordinary differential equations
- Global asymptotic stability
- Global injectivity
- Difference equations
- Cima, A. Gasull, F. Mañosas. A simple solution of some composition conjectures for Abel equations. J. Math. Anal. Appl., 398, 477-486, 2013
- Gasull, C. Li, J. Torregrosa. A new Chebyshev family with applications to Abel equations. J. Differential Equations, 252, 1635-1641, 2012
- Gasull, H. Giacomini, J. Torregrosa. Some results on homoclinic and heteroclinic connections in planar systems. Nonlinearity, 23, 2977-3001, 2010
- Cima, A. Gasull, V. Mañosas. Studying discrete dynamical systems through differential equations. J. Differential Equations, 244, 630-648, 2008
- Freire, A. Gasull, A. Guillamon. First derivative of the period function with applications. J. Differential Equations, 204, 139-162, 2004