Juan Luis García Guirao is Full Professor of Applied Mathematics at Technical University of Cartagena in Spain. He obtained his Degree in Mathematics at Universidad de Murcia (Spain) in 2001. Covering all the subjects of the Degree in four years, he used the last one for working on his Master Thesis. Under the supervision of Professor Francisco Balibrea, Full Professor of Mathematical Analysis and founder the Dynamical Systems Group of the Region of Murcia (http://www.um.es/sistdinamicos) he defended his Master Thesis in 2001 and PhD Thesis in 2004. The PhD had European Mention and the predoctoral research stay was done at Instituto Superior Tecnico in Lisbon under the supervision of Professor José Sousa-Ramos, one of the main researchers in Dynamical Systems in Portugal, who passed away in 2007.
He has several positions in different universities: Universidad de Alicante, Universidad de Castilla-La Mancha, Universidad Autónoma de Barcelona and Universidad Politécnica de Cartagena (now).
In 2011, he became in the youngest Mathematics Full Professor in Spain with 33 years old. Author of more than 250 research papers published in the best journals he has supervised 5 PhD Thesis and more than 11 Master Thesis/Final Degree Jobs. He belongs to the Editorial Board of several journals, between them MATCH Commun. Math. Comput. Chem. ranked in first position of the JCR 2010 list (Interdisciplinary Mathematics). Founder and Editor in Chief of Applied Mathematics and Nonlinear Sciences (Sciendo) he has been awarded with several international prizes as NSP 2017 prize and 2018 Best paper Award from Differences Equations Society joint with Jaume Llibre. Now, he is Head of Dynamical Systems Group of Region of Murcia.
There are three research lines opened: discrete dynamical systems defined in low dimensional spaces, study of the periodic structure of smooth systems using the homological Lefschetz theory and analysis of Hamiltonian systems. Applications of the previous lines to problems coming from the fields of economy, chemistry and engineering are considered.
In 2020 was elected as a Distinguish Professor by King Abdulaziz University recognizing his deep contribution to Dynamical Systems. In July 2021 has been selected as Director of the Chair Primafrio 4.0 at Technical University of Cartagena where he is coordinating the research activities of this logistic group, the biggest one in Europe in the transportation of refrigerated goods by road in trucks. In 2022 was elected by Stanford as Highly Cited Researcher Top 2%.
A review on the Hill problem: Periodic solutions of the spatial lunar and of the perturbed spatial quantized Hill problems
The aim of the present talk is to present the main characteristics of the so-called Hill problem. We shall discuss some perturbation approaches, such as the classical perturbation theory, Poincaré–Lindstedt technique, multiple scales method, the KB averaging method, and averaging theory. In the case of the spatial lunar and of the perturbed spatial quantized Hill problems we shall present the necessary conditions to construct the periodic solutions emerging from the equilibrium points for the spatial Hill problem under the perturbation effect of quantum corrections.