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Konstantinos Efstathiou

Konstantinos Efstathiou

Associate Professor of Mathematics at Duke Kunshan University
DKU Faculty

Selected Publications

Entrainment degree of globally coupled Winfree oscillators under external forcing.

Journal Article Chaos (Woodbury, N.Y.) · October 2022 Featured Publication We consider globally connected coupled Winfree oscillators under the influence of an external periodic forcing. Such systems exhibit many qualitatively different regimes of collective dynamics. Our aim is to understand this collective dynamics and, in part ... Full text Cite

Loops of Infinite Order and Toric Foliations

Journal Article Regular and Chaotic Dynamics · May 1, 2022 Featured Publication In 2005 Dullin et al. proved that thenonzero vector of Maslov indices is an eigenvector with eigenvalue1 of the monodromy matrices of an integrable Hamiltonian system.We take a close look at the geometry behind this result and extendit to the more general ... Full text Cite

Persistent homology of the cosmic web-I. Hierarchical topology in ΛcDM cosmologies

Journal Article Monthly Notices of the Royal Astronomical Society · October 1, 2021 Using a set of Lambda cold dark matter simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow ... Full text Cite

Synchronized clusters in globally connected networks of second-order oscillators: Uncovering the role of inertia.

Journal Article Chaos (Woodbury, N.Y.) · September 2021 Featured Publication We discuss the formation of secondary synchronized clusters, that is, small clusters of synchronized oscillators besides the main cluster, in second-order oscillator networks and the role of inertia in this process. Such secondary synchronized clusters giv ... Full text Cite

Recent advances in the monodromy theory of integrable Hamiltonian systems

Journal Article Indagationes Mathematicae · February 1, 2021 The notion of monodromy was introduced by J.J. Duistermaat as the first obstruction to the existence of global action coordinates in integrable Hamiltonian systems. This invariant was extensively studied since then and was shown to be non-trivial in variou ... Full text Cite

Hamiltonian Monodromy and Morse Theory

Journal Article Communications in Mathematical Physics · April 1, 2020 We show that Hamiltonian monodromy of an integrable two degrees of freedom system with a global circle action can be computed by applying Morse theory to the Hamiltonian of the system. Our proof is based on Takens’s index theorem, which specifies how the e ... Full text Cite

Reduction of oscillator dynamics on complex networks to dynamics on complete graphs through virtual frequencies.

Journal Article Physical review. E · February 2020 We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual frequencies we s ... Full text Cite

Bifurcations and monodromy of the axially symmetric 1:1:−2 resonance

Journal Article Journal of Geometry and Physics · December 1, 2019 We consider integrable Hamiltonian systems in three degrees of freedom near an elliptic equilibrium in 1:1:−2 resonance. The integrability originates from averaging along the periodic motion of the quadratic part and an imposed rotational symmetry about th ... Full text Cite

Scattering invariants in Euler's two-center problem

Journal Article Nonlinearity · March 12, 2019 The problem of two fixed centers was introduced by Euler as early as in 1760. It plays an important role both in celestial mechanics and in the microscopic world. In the present paper we study the spatial problem in the case of arbitrary (both positive and ... Full text Cite

A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy

Journal Article Journal of Mathematical Physics · March 1, 2019 The isotropic harmonic oscillator in dimension 3 separates in several different coordinate systems. Separating in a particular coordinate system defines a system of three Poisson commuting integrals and, correspondingly, three commuting operators, one of w ... Full text Cite

Self-consistent method and steady states of second-order oscillators

Journal Article Physical Review E · October 1, 2018 The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks, complications to the application of the self-consistent method arise be ... Full text Cite

A Study of the Effect of Doughnut Chart Parameters on Proportion Estimation Accuracy

Journal Article Computer Graphics Forum · September 1, 2018 Pie and doughnut charts nicely convey the part–whole relationship and they have become the most recognizable chart types for representing proportions in business and data statistics. Many experiments have been carried out to study human perception of the p ... Full text Cite

Parallel Transport Along Seifert Manifolds and Fractional Monodromy

Journal Article Communications in Mathematical Physics · December 1, 2017 The notion of fractional monodromy was introduced by Nekhoroshev, Sadovskií and Zhilinskií as a generalization of standard (‘integer’) monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the present paper we prove a ge ... Full text Cite

Isochronous dynamics in pulse coupled oscillator networks with delay.

Journal Article Chaos (Woodbury, N.Y.) · May 2017 We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions-subsets of the phase space filled with periodic orbi ... Full text Cite

Monodromy of Hamiltonian systems with complexity 1 torus actions

Journal Article Journal of Geometry and Physics · May 1, 2017 We consider the monodromy of n-torus bundles in n degree of freedom integrable Hamiltonian systems with a complexity 1 torus action, that is, a Hamiltonian Tn−1 action. We show that orbits with T1 isotropy are associated to non-trivia ... Full text Cite

Rotation forms and local hamiltonian monodromy

Journal Article Journal of Mathematical Physics · February 1, 2017 The monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article, we give a genera ... Full text Cite

CAST: Effective and Efficient User Interaction for Context-Aware Selection in 3D Particle Clouds.

Conference IEEE transactions on visualization and computer graphics · January 2016 We present a family of three interactive Context-Aware Selection Techniques (CAST) for the analysis of large 3D particle datasets. For these datasets, spatial selection is an essential prerequisite to many other analysis tasks. Traditionally, such interact ... Full text Cite

The boundary-hopf-fold bifurcation in filippov systems

Journal Article SIAM Journal on Applied Dynamical Systems · January 1, 2015 This paper studies the codimension-3 boundary-Hopf-fold (BHF) bifurcation of planar Filippov systems. Filippov systems consist of at least one discontinuity boundary locally separating the phase space to disjoint components with different dynamics. Such sy ... Full text Cite

Uncovering Fractional Monodromy

Journal Article Communications in Mathematical Physics · December 1, 2013 The uncovering of the role of monodromy in integrable Hamiltonian fibrations has been one of the major advances in the study of integrable Hamiltonian systems in the past few decades: on one hand monodromy turned out to be the most fundamental obstruction ... Full text Cite

Efficient Structure-Aware Selection Techniques for 3D Point Cloud Visualizations with 2DOF Input.

Journal Article IEEE transactions on visualization and computer graphics · December 2012 Data selection is a fundamental task in visualization because it serves as a pre-requisite to many follow-up interactions. Efficient spatial selection in 3D point cloud datasets consisting of thousands or millions of particles can be particularly challengi ... Full text Cite

The topology associated with cusp singular points

Journal Article Nonlinearity · December 1, 2012 In this paper we investigate the global geometry associated with cusp singular points of two-degree of freedom completely integrable systems. It typically happens that such singular points appear in couples, connected by a curve of hyperbolic singular poin ... Full text Cite

Pacer cell response to periodic Zeitgebers

Journal Article Physica D Nonlinear Phenomena · September 15, 2011 Almost all organisms show some kind of time periodicity in their behavior. In mammals, the neurons of the suprachiasmatic nucleus form a biological clock regulating the activityinactivity cycle of the animal. The main question is how this clock is able to ... Full text Cite

A geometric fractional monodromy theorem

Conference Discrete and Continuous Dynamical Systems Series S · December 1, 2010 We prove the existence of fractional monodromy for two degree of freedom integrable Hamiltonian systems with one-parameter families of curled tori under certain general conditions. We describe the action coordinates of such systems near curled tori and we ... Full text Cite

Normalization and global analysis of perturbations of the hydrogen atom

Journal Article Reviews of Modern Physics · August 3, 2010 The hydrogen atom perturbed by sufficiently small homogeneous static electric and magnetic fields of arbitrary mutual alignment is a specific perturbation of the Kepler system with three degrees of freedom and three parameters. Normalization of the Kepleri ... Full text Cite

Fractional bidromy in the vibrational spectrum of HOCl.

Journal Article Physical review letters · March 2010 We introduce the notion of fractional bidromy which is the combination of fractional monodromy and bidromy, two recent generalizations of Hamiltonian monodromy. We consider the vibrational spectrum of the HOCl molecule which is used as an illustrative exam ... Full text Cite

Integrable Hamiltonian systems with swallowtails

Journal Article Journal of Physics A: Mathematical and Theoretical · February 26, 2010 Full text Cite

Complete classification of qualitatively different perturbations of the hydrogen atom in weak near-orthogonal electric and magnetic fields

Journal Article Journal of Physics A Mathematical and Theoretical · April 20, 2009 We consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields in near-orthogonal configurations. Normalization of the Keplerian symmetry reveals that in the parameter space such systems belong in a 'zo ... Full text Cite

Most typical 1 ratio 2 resonant perturbation of the hydrogen atom by weak electric and magnetic fields.

Journal Article Physical review letters · December 2008 We study a perturbation of the hydrogen atom by small homogeneous static electric and magnetic fields in a specific mutual alignment with angle approximately pi/3 which results in the 1 ratio 2 resonance of the linearized Keplerian n-shell approximation. T ... Full text Cite

Heteroclinic cycles between unstable attractors

Journal Article Nonlinearity · June 1, 2008 We consider networks of pulse coupled linear oscillators with non-zero delay where the coupling between the oscillators is given by the Mirollo-Strogatz function. We prove the existence of heteroclinic cycles between unstable attractors for a network of fo ... Full text Cite

Robustness of unstable attractors in arbitrarily sized pulse-coupled networks with delay

Journal Article Nonlinearity · February 7, 2008 We consider arbitrarily large networks of pulse-coupled oscillators with non-zero delay where the coupling is given by the Mirollo-Strogatz function. We prove that such systems have unstable attractors (saddle periodic orbits whose stable set has non-empty ... Full text Cite

Classification of perturbations of the hydrogen atom by small static electric and magnetic fields

Journal Article Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · July 8, 2007 We consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields of all possible mutual orientations. Normalizing with regard to the Keplerian symmetry, we uncover resonances and conjecture that the param ... Full text Cite

Fractional monodromy in the 1 : - 2 resonance

Journal Article Advances in Mathematics · February 15, 2007 We give an analytic proof of the fractional monodromy theorem for the 1 : - 2 oscillator system with S1 symmetry formulated by N.N. Nekhoroshev, D.A. Sadovskií, and B.I. Zhilinskií in C. R. Acad. Sci. Paris, Ser. I 335 (2002) 985-988. Our proof ... Full text Cite

Escapes and recurrence in a simple Hamiltonian system

Journal Article Celestial Mechanics and Dynamical Astronomy · August 26, 2004 Many physical systems can be modeled as scattering problems. For example, the motions of stars escaping from a galaxy can be described using a potential with two or more escape routes. Each escape route is crossed by an unstable Lyapunov orbit. The region ... Full text Cite

Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields

Journal Article Physica D Nonlinear Phenomena · July 15, 2004 We consider the hydrogen atom in crossed electric and magnetic fields. We prove that near the Stark and Zeeman limits the system goes through two qualitatively different Hamiltonian Hopf bifurcations. We explain in detail the geometry of the bifurcations. ... Full text Cite

Perturbations of the 1:1:1 resonance with tetrahedral symmetry: A three degree of freedom analogue of the two degree of freedom Hénon-Heiles Hamiltonian

Journal Article Nonlinearity · March 1, 2004 We study a class of three degree of freedom (3-DOF) Hamiltonian systems that share certain characteristics with the 2-DOF Hénon-Heiles Hamiltonian. Our systems represent a 1:1:1 resonant three-oscillator whose principal nonlinear perturbation is the cubic ... Full text Cite

Analysis of rotation-vibration relative equilibria on the example of a tetrahedral four atom molecule

Journal Article SIAM Journal on Applied Dynamical Systems · January 1, 2004 We study relative equilibria (RE) of a nonrigid molecule, which vibrates about a well-defined equilibrium configuration and rotates as a whole. Our analysis unifies the theory of rotational and vibrational RE. We rely on the detailed study of the symmetry ... Full text Cite

Global bending quantum number and the absence of monodromy in the HCN↔CNH molecule

Journal Article Physical Review A Atomic Molecular and Optical Physics · January 1, 2004 The vibrational potential of HCN/CNH isomerized molecule was analyzed using model system based on deformation of spherical pendulum. This model was used to reproduce large amplitude bending vibrations of flexible triatomic molecules with two stable linear ... Full text Cite

Linear Hamiltonian Hopf bifurcation for point-group-invariant perturbations of the 1:1:1 resonance

Journal Article Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · December 8, 2003 We consider G x R-invariant Hamiltonians H on complex projective 2-space, where G is a point group and R is the time-reversal group. We find the symmetry-induced stationary points of H and classify them in terms of their linear stability. We then determine ... Full text Cite

Orbits in the H(2)O molecule.

Journal Article Chaos (Woodbury, N.Y.) · June 2001 We study the forms of the orbits in a symmetric configuration of a realistic model of the H(2)O molecule with particular emphasis on the periodic orbits. We use an appropriate Poincare surface of section (PSS) and study the distribution of the orbits on th ... Full text Cite

A method for accurate computation of the rotation and the twist numbers of invariant circles

Journal Article Physica D Nonlinear Phenomena · January 1, 2001 A method is proposed for accurate evaluation of the rotation and the twist numbers of invariant circles in two degrees of freedom Hamiltonian systems or two-dimensional symplectic maps. The method uses the recurrence of orbits to overcome the problems usua ... Full text Cite