Researcher

Jaume Alonso Fernandez

Research Expertise:My research lies at the intersection of dynamical systems and symplectic geometry. More concretely, I work with semitoric systems, a specific type of completely integrable Hamiltonian systems defined on 4-dimensional symplectic manifolds, where one of the conserved quantities induces a global circular action and other additional conditions. These systems can be classified using five symplectic invariants, but their computation is troublesome. I develop computational methods to calculate them with mathematical software, using properties of elliptic integrals and the theory of complex elliptic curves.

Keywords:SEMITORIC SYSTEMS, DYNAMICAL SYSTEMS, INTEGRABLE SYSTEMS, SYMPLECTIC GEOMETRY, ELLIPTIC CURVES, Mathematics

Disciplines:Dynamical systems and ergodic theory, Ordinary differential equations, Mechanics of particles and systems, Global analysis, analysis on manifolds, Classical mechanics, Analytic aspects and differential equations of physics, Classical and quantum integrable systems, Geometric aspects of physics

Research techniques:IT tools: Mathematica, Latex, beamer Mathematical tools: Arnold-Liouville's theorem, elliptic curves, real and complex elliptic integrals, Legendre's canonical forms, Eliasson's normal forms

Users of research expertise:Quantum physicists and chemists working with systems that have monodromy. Physicists working on models that preserve quantities (energy, angular momentum, etc)