Journal
A paper with Bohuan Lin and Holger Waalkens on toric foliations has been published in Regular and Chaotic Dynamics. From the paper:
In 2005 Dullin et al. proved that the non zero vector of Maslov indices is an eigenvector with eigenvalue 1 of the monodromy matrices of an integrable Hamiltonian system. We take a close look at the geometry behind this result and extend it to the more general context of possibly non-Hamiltonian systems. We construct a bundle morphism defined on the lattice bundle of an (general) integrable system, which can be seen as a generalization of the vector of Maslov indices. The nontriviality of this bundle morphism implies the existence of common eigenvectors with eigenvalue 1 of the monodromy matrices, and gives rise to a corank 1 toric foliation refining the original one induced by the integrable system. Furthermore, we show that, in the case where the system has 2 degrees of freedom, this implies the existence of a compatible free $S^1$ action on the regular part of the system.
The last paper with Jian Gao on the collective dynamics of second-order oscillators has been accepted for publication in Chaos. From the paper:
The synchronization process in oscillator networks, such as in the Kuramoto model, is typically driven by the formation of a large synchronized cluster that gradually absorbs more oscillators. This process can be disrupted by the formation of smaller synchronized clusters that compete with the main one. Such smaller clusters lead to non-stationary states where the order parameter varies periodically in time in contrast to coherent stationary states where it is constant. In this paper, we consider oscillators with inertia and we study the formation of smaller synchronized clusters. We find that inertia plays a crucial role in the formation of such clusters and the increase of inertia leads to a strengthening of the secondary clusters at the expense of the main cluster. We use numerical experiments, a theoretical analysis of the mean-field equations, and a simplified model to explain different aspects of the formation of secondary synchronized clusters and non-stationary states.
A paper with Georg Wilding, Keimpe Nevenzeel, Rien van de Weygaert, Gert Vegter, Pratyush Pranav, Bernard Jones, and Job Feldbrugge on the persistent homology of the large scale structures in ΛCDM cosmological models has been accepted for publication in the Monthly Notices of the Royal Astronomical Society. More details and the paper can be found here.
Jian Gao, my third PhD student, successfully defended today his PhD thesis on the Synchronization of coupled second-order Kuramoto oscillators. Congratulations Dr. Gao 😄!
Yongjiao Zhang, my second PhD student, successfully defended last Monday her thesis on externally forced Winfree systems at the University of Groningen. Congratulations Dr. Zhang!
The opening conference of the Zu Chongzhi Research Center for Mathematics and Computational Sciences takes place October 31 to November 3, 2019 at Duke Kunshan University. I am giving a talk with title On the topology of integrable Hamiltonian fibrations.
Starting October 1st, 2019 I will be appointed Associate Professor of Mathematics at the Zu Chongzhi Center for Mathematics and Computational Sciences of Duke Kunshan University in Kunshan, China.
I will give a talk on Rotation Forms and Non-compact Standard and Fractional Monodromy at the mini-workshop Semitoric Systems and Beyond. The mini-workshop takes place 10-11 September 2019 in Antwerp on the occasion of the PhD defense of Jaume Alonso.
I will give a talk on Bifurcations and Monodromy of the Axially Symmetric 1:1:-2 Resonance at the mini-symposium Integrable Hamiltonian Systems in Equadiff 2019. Equadiff 2019 takes place 8-12 July 2019 in Leiden. The mini-symposium is organized by Holger Waalkens and Alexey Bolsinov.
The Mathematics for Real World Systems (MathSys) Centre for Doctoral Training at the University of Warwick and the Data Science and Systems Complexity Centre at the University of Groningen are co-organizing a PhD Summer School on Complex Networks: Dynamics and Control.
The school will take place 3-5 July 2019 at the University of Warwick. I will give two lectures on the Dynamics and Synchronization of Globally Coupled Oscillators.
More information can be found on the school website.
I gave a presentation on Hamiltonian Monodromy at the Symplectic Dynamics workshop that took place 8-12 April 2019 at the Lorentz Center. The workshop was organized by Urs Frauenfelder, Holger Waalkens, and Lei Zhao.
On the occasion of the PhD defense of Nikolay Martynchuk we are organizing a mini-workshop in Groningen on Thursday 20 September 2018 with talks by Alexey Bolsinov, Holger Dullin, Sonja Hohloch, Andreas Knauf, San Vũ Ngọc, and Nikolay Martynchuk. More information is available on the workshop website. The PhD defense will take place on Friday 21 September at 11:00.