Journal

In 2010 I continued working on research problems on dynamical systems and the geometry of integrable Hamiltonian fibrations. Here is a short list of 2010 events. Four papers, finished in the previous year, were published in 2010. Two more papers, one on a covering spaces approach to fractional Hamiltonian monodromy and the other on circadian rhythms, were finished and are now under review. Started a collaboration with Andrea Giacobbe which in 2010 brought Andrea once to Groningen and me once to Padova.

This week (22-26 November) I am visiting the Mathematics department1 in Padova to work with Andrea Giacobbe and Francesco Fassò; I am also giving a seminar on “Generalized Hamiltonian monodromy and applications”. The Mathematics department is, since a few years ago, housed in ‘Torre Archimede’. Being Greek, I of course like the name. But since Archimedes had never been in Padova, ‘Torre Levi-Civita’ would have probably been a more appropriate name.

Teaching period is over. During this period I was invited to give two talks but I didn´t have until now the opportunity to write about these here. In both occasions I talked about my favorite subject at the moment: integrable Hamiltonian systems with codimension-1 singularities. Firstly, I was invited to give a talk at the second meeting of the GDR Quantum Dynamics that took place 24-26 March 2010 in Dijon. Besides my presentation, I had the opportunity to discuss with my colleagues in Dijon (Dominique Sugny, Pavao Mardešić, Michèle Pelletier, and Hans Jauslin) and with Dmitrií Sadovskií.

Three new papers have been accepted for publication recently. First, a review paper with Dmitrií Sadovskií has been accepted for publication in Reviews of Modern Physics. The subject of the review is the recent advances in the study of the hydrogen atom in electric and magnetic fields that were made possible by adopting the point of view of global analysis of (near) integrable Hamiltonian systems. A paper on bidromy with Dominique Sugny has been already published in Journal of Physics A.

I´m just back from my vacation trip to the very beautiful Iceland, so the new year (in terms of work) starts a little late. I have realized that time plays very strange tricks with my memories and as I grow older things become worse. In particular, when I look back I tend to underestimate the things I have achieved in any given time period and how much I have developed as a researcher and as a person.

The main requirement for numerical code is that it must be fast. This means that numerical code is usually written in some “low-level” language such as C or Fortran. Such code can be highly optimized but low-level languages are not very expressive (where expressiveness is defined as the inverse of the number of lines of code that is necessary in order to express a program). Thus they are not very well suited to other tasks, such as data I/O, command line argument parsing, graphics, and user interaction that are peripheral to, but nevertheless important for, the computation and where speed does not play the primary role.

I have been unhappy for some time now with the function that I had written in Mathematica for computing the normal form of a Hamiltonian system. I used the standard Lie series approach but I had written the code using a traditional approach with several Do loops. Except for the fact that this kind of code is completely contrary to Mathematica´s philosophy I found the code hard to read and inefficient to the degree at least that Mathematica can be efficient.

On June 23 2009 I gave a talk on «Unstable attractors in pulse coupled oscillator networks» in the workshop Brain Waves. The workshop is organized in the Lorentz Center by Stan Gielen, Stephan van Gils, Michel van Putten, and David Terman.

The workshop on Monodromy and geometric phases in classical and quantum mechanics took place June 15-19 2009 at the Lorentz Center in Leiden. I enjoyed preparing the workshop and bringing together people from different fields. The talks were great and I would like to thank the speakers for making this workshop a success. My coorganizers Jonathan Robbins, Dmitrií Sadovskií, and Holger Waalkens shared the weight. And I would like to thank also Martje Kruk and Gerda Filippo from the Lorentz Center for taking care of all the practical aspects of the workshop.

On May 12 2009 I give a talk in the conference Singularities of Planar Vector Fields, Bifurcations and Applications on «Hamiltonian monodromy». The conference is organized by Pavao Mardesic and Christiane Rousseau.

Between 22-24 April 2009 I visit the group of Carles Simò in Barcelona. I will give a presentation in the UB-UPC DSG Seminar on «The hydrogen atom in electric and magnetic fields».

The paper with Olga Lukina and Dmitrií Sadovskií on «Complete classification of qualitatively different perturbations of the hydrogen atom in weak near orthogonal electric and magnetic fields» has been accepted for publication in Journal of Physics A.