Journal

The workshop Spectral Analysis, Stability and Bifurcation in Modern Nonlinear Physical Systems took place at the Banff International Research Station between 4 and 9 November 2012. In the workshop I gave an invited talk on the recent work about using covering maps to prove fractional monodromy in 2-DOF integrable Hamiltonian systems in \(n_1{:}-n_2\) resonance. The video of the presentation is available from the BIRS website.

Our paper with Andrea Giacobbe on cusp singularities of integrable Hamiltonian fibrations has now been accepted for publication in Nonlinearity. Andrea and I tried to understand how cusp singularities fit together in the momentum domain of integrable Hamiltonian fibrations. It turns out that when two cusp singularities are connected by a curve of hyperbolic singularities there are locally two possible topologies of the unfolded momentum domain that we call pleat and flap.

The paper on efficient structure-aware selection techniques for 3D point clouds that will be presented at Visweek'12, taking place in Seattle, was selected for a Honorable Mention award.

George Efstathiou was born on 15 August 2012 at 13:36 at the Martini Hospital in Groningen. His weight was 2.63kg and his length 48cm. Lingyun and George are both doing fine.

And now for something completely different. Occasionally I do things that fall outside my main research interests. One of these things is a recent work with Lingyun Yu, Petra Isenberg, and Tobias Isenberg where we tried to develop intuitive computer algorithms for the interactive selection of particle clusters in 3D particle datasets. We were motivated in this effort by the problem of selecting clusters in N-body galaxy simulations but the algorithms we developed can be applied in other domains that deal with 3D particle datasets.

The conference 5th Shanghai International Symposium on Nonlinear Sciences and Applications took place last week at the Fudan University in Shanghai and on a cruise from Yichang to Chongqing along the Yangtze river. In the conference I gave an invited talk with title «Synchronization in biological systems» where I presented the work [1,2] on pulse-coupled oscillator systems with delay I have done in collaboration with Easwar Subramanian and Henk Broer.

In the period 7-17 May 2012 I visited the Université de Bourgogne in Dijon for a collaboration with Robert Roussarie on the regularization of discontinuous dynamical systems.

On December 19-20, 2011 the Brain-Mind workshop took place at Fudan University in Shanghai. In the workshop I presented one of the invited keynotes. The title of my talk was “Applications of dynamical systems in biology and synchronization”. The concept of synchronization plays a very important role in biology. In the talk I presented two systems that exhibit synchronization. The first such system is a network of pulse coupled oscillators with delay.

Recently Domien Beersma, Henk Broer, Kim Gargar, Igor Hoveijn, and I published in Physica D a paper on synchronization and circadian rhythms. The basic idea behind the paper is to study in a simple model how a single pacer cell synchronizes to a periodic signal. This signal includes the effect of the external environment (light-dark cycle) but also the effect of the rest of the pacer cells. It turns out that such system can be described by a family of circle maps.

The conference Symmetry and Perturbation Theory 2011 took place last week in Otranto. The conference was organized by Giuseppe Gaeta, Ferdinand Verhulst, Raffaele Vitolo, and Sebastian Walcher. In the conference I gave an invited talk with title «Uncovering fractional monodromy» presenting a work I am doing in collaboration with Henk Broer. The main idea behind this work is that when dealing with systems that have fractional monodromy it is more natural to first lift them to a branched covering space.

On 31 January and 1 February 2011, Henk Broer, Xia Liu, and I, organize a workshop with subject Resonance and Synchronization. The purpose of the workshop is to explore the interaction between these two dynamical concepts and their applications in biological and mechanical systems. More information about the workshop including information about registration and about the program is available on the workshop’s website .

Between 14 and 20 January 2011 I am visiting Andrea Giacobbe and Francesco Fassò at the Mathematics department in Padova to continue the work we did during my previous visit.