Phone 619977199
E-mail xavier.jarque@ub.edu
Position Professor at UB
Research interests Applied Math
Area Dynamical Systems
Jarque i Ribera, Xavier
Biosketch

Dr. Xavier Jarque is a professor at Universitat de Barcelona (UB), which he joined in 2003 (on leave at Universitat Rovira i Virgili, Tarragona, from 2008 to 2010). Hi did the Pd.D. at Universitat Autònoma de Barcelona and he spent two years at Boston University (Boston, MA) as post-doctoral fellowship. As a researcher he has focussed in holomorphic dynamics, more concretly in transcendental dynamics as discrete dynamical systems genereted by the iterates of transcendental meromorphic maps. He is member of the research group HOLODYN (http://www.maia.ub.es/holodyn/) and GSD-UAB (http://www.gsd.uab.cat/). Since 2003 has had taught, among other subjects, Differential Equations, Dynamical Systems and Numerical Analysis. During the last 10 years he had taught (joint with Ernest Fontich) the Dynamical Systems course at the Master in Advanced Mathematics. Further information at: http://www.maia.ub.es/~xjarque

Interests

Dynamical system and holomorphic dynamics

Projects

2017SGR1374 (Generalitat de Catalunya; Grup Consolidat en sistemes dinàmics. IP: Àngel Jorba. Període 2017-21).

PID2020-118281GB-C32 (Ministerio de Ciencia y Innovación. IP: Núria Fagella i Lluís Alsedà. Període 2021-23).

MDM-2014-0445 (Ministerio de  Ciencia y Innovación. IP: Marcos Noy. Període 2015-19).

2012/06/M/ST1/00168 (Polish Academia of Science. IP: Krzysztof Baranski i Núria Fagella. Període 2013-15).

 

Selected publications


Topological properties of the immediate basins of attraction for the secant method (with with L. Gardini add A. Garijo.), Mediterranean Journal of Mathematics, 18(5), 221, 2021.
(This is the a good reference on the dynamical plane of the Secant method, as a dynamical system in R^2. Toni and I did it in Trento while visiting Laura. Nice remembers; with the exception of the 4-0 against Liverpool in the Champions League)

Connectivity of Julia sets of Newton maps: A unified approach (with with K. Barański, N. Fagella and B. Karpińska.), Revista Matemática Iberoamericana, 34(3), 1211-1228, 2018. (In this paper we show, in a direct way, that the Julia set of ANY Newton's map is connected; uau!!)

On the connectivity of the Julia set for meromorphic transcendental functions(with K. Baranski, N. Fagella and B. Karpinska), Inventiones Mathematicae 198(3), pp 591-636, 2014 (A solution of an old problem about the existence of absorbing domains for general hyperbolic domains and applications to the connectivity of the Julia set for meromorphic functions)

Burshing the hairs of transcendental entire functions (with K. Baranski and L. Rempe), Topology and its Applications, 159(8), pp.2102–2114, 2012. (A generalisation of the remarkable paper "The geometry of the Julia sets", Aarts and Oversteegen, Trans. AMS 1993)

On the connectivity of the escaping set for complex exponential Misiurewicz parameters, Proceedings of the AMS 139(6), pp. 2057–2065, 2011. (A nice counterintuitive result and my only paper alone)

On the period function for a family of complex differential equations (with A. Garijo and A. Gasull), Journal of Differential Equations, 224(2) pp. 314–331, 2006. (The three authors worked together for a series of years, and this is our best result)

Spatial competition with concave transport costs (with M.A. de Frutos and H. Hamoudi), Regional Sciences and Urgan Economics, 32 (4) pp. 531–540, 2002. (My preferable paper in Mathematical Economics)

Hamiltonian stability in the plane (with Z. Nitecki), Ergodic Theory Dynamical Systems, 20 (3) pp. 775–799, 2000. (A nice continuation of my Ph. D.)

Misiurewicz points for complex exponentials (with R.L. Devaney) International Journal of Bifurcation and Chaos, 7(7). 1599–1614, 1997. (My first paper in complex dynamics)

Structural stability of planar Hamiltonian polynomial vector fields (with J. Llibre) Proceedings of the London Mathematical Society, 68(3). 617–640, 1994. (My first paper and the best result of my Ph.D.)