Publications

Monograph

• Metamorphoses of Hamiltonian Systems with Symmetries. K. Efstathiou. Lecture Notes in Mathematics, 1864, Springer (2005).
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Journal Articles

• Recent advances in the monodromy theory of integrable Hamiltonian systems. N. Martynchuk, H. W. Broer, K. Efstathiou. Indagationes Mathematicae, N/A, N/A (2020).
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• Reduction of oscillator dynamics on complex networks to dynamics on complete graphs through virtual frequencies. J. Gao, K. Efstathiou. Physical Review E, 101(2), 022302 (2020).
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• Hamiltonian monodromy and Morse theory. N. Martynchuk, H. W. Broer, K. Efstathiou. Communications in Mathematical Physics, 375(2), 1373-1392 (2020).
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• Bifurcations and monodromy of the axially symmetric 1:1:-2 resonance. K. Efstathiou, H. Hanßmann, A. Marchesiello. Journal of Geometry and Physics, 146, 103493 (2019).
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• A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy. I. Chiscop, H. R. Dullin, K. Efstathiou, H. Waalkens. Journal of Mathematical Physics, 60(3), 032103 (2019).
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• Scattering invariants in Euler's two-center problem. N. Martynchuk, H. R. Dullin, K. Efstathiou, H. Waalkens. Nonlinearity, 32(4), 1296-1326 (2019).
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• Self-consistent method and steady states of second-order oscillators. J. Gao, K. Efstathiou. Physical Review E, 98(4), 042201 (2018).
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• A study of the effect of doughnut chart parameters on proportion estimation accuracy. X. Cai, K. Efstathiou, X. Xie, Y. Wu, Y. Shi, L. Yu. Computer Graphics Forum, 37(6), 300-312 (2018).
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• Parallel transport along Seifert manifolds and fractional monodromy. N. Martynchuk, K. Efstathiou. Communications in Mathematical Physics, 356(2), 427-449 (2017).
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• Isochronous dynamics in pulse coupled oscillator networks with delay. P. Li, W. Lin, K. Efstathiou. Chaos, 27(5), 053103 (2017).
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• Rotation forms and local Hamiltonian monodromy. K. Efstathiou, A. Giacobbe, P. Mardešić, D. Sugny. Journal of Mathematical Physics, 58(2), 022902 (2017).
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• Monodromy of Hamiltonian systems with complexity 1 torus actions. K. Efstathiou, N. Martynchuk. Journal of Geometry and Physics, 115, 104-115 (2017).
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• CAST: effective and efficient user interaction for context-aware selection in 3D particle clouds. L. Yu, K. Efstathiou, P. Isenberg, T. Isenberg. IEEE Transactions on Visualization and Computer Graphics, 22(1), 886-895 (2016).
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• The Boundary-Hopf-Fold bifurcation in Filippov systems. K. Efstathiou, X. Liu, H. W. Broer. SIAM Journal on Applied Dynamical Systems, 14(2), 914-941 (2015).
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• Uncovering fractional monodromy. K. Efstathiou, H. W. Broer. Communications in Mathematical Physics, 324(2), 549-588 (2013).
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• The topology associated to cusp singular points. K. Efstathiou, A. Giacobbe. Nonlinearity, 25(12), 3409-3422 (2012).
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• Efficient structure-aware selection techniques for 3D point cloud visualizations with 2DOF input. L. Yu, K. Efstathiou, P. Isenberg, T. Isenberg. IEEE Transactions on Visualization and Computer Graphics, 18(12), 2245-2254 (2012).
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• Pacer cell response to periodic Zeitgebers. D. G. M. Beersma, H. W. Broer, K. Efstathiou, K. A. Gargar, I. Hoveijn. Physica D, 240, 1516-1527 (2011).
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• Integrable Hamiltonian systems with swallowtails. K. Efstathiou, D. Sugny. Journal of Physics A, 43(8), 085216 (2010).
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• Fractional bidromy in the vibrational spectrum of HOCl. E. Assémat, K. Efstathiou, M. Joyeux, D. Sugny. Physical Review Letters, 104(11), 113002 (2010).
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• Normalization and global analysis of perturbations of the hydrogen atom. K. Efstathiou, D. A. Sadovskií. Reviews of Modern Physics, 82(3), 2099-2154 (2010).
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• A geometric fractional monodromy theorem. H. W. Broer, K. Efstathiou, O. V. Lukina. Discrete and Continuous Dynamical Systems - Series S (DCDS-S), 3(4), 517-532 (2010).
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• Complete classification of qualitatively different perturbations of the hydrogen atom in weak near-orthogonal electric and magnetic fields. K. Efstathiou, O. V. Lukina, D. A. Sadovskií. Journal of Physics A, 42(5), 055209 (2009).
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• Most typical 1:2 resonant perturbation of the hydrogen atom by weak electric and magnetic fields. K. Efstathiou, O. V. Lukina, D. A. Sadovskií. Physical Review Letters, 101(25), 253003 (2008).
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• Robustness of unstable attractors in arbitrarily sized pulse-coupled networks with delay. H. W. Broer, K. Efstathiou, E. Subramanian. Nonlinearity, 21(1), 13-49 (2008).
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• Heteroclinic cycles between unstable attractors. H. W. Broer, K. Efstathiou, E. Subramanian. Nonlinearity, 21(6), 1385-1410 (2008).
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• Fractional monodromy in the 1:-2 resonance. K. Efstathiou, R. H. Cushman, D. A. Sadovskií. Advances in Mathematics, 209(1), 241-273 (2007).
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• Classification of perturbations of the hydrogen atom by small static electric and magnetic fields. K. Efstathiou, D. A. Sadovskií, B. I. Zhilinskií. Proceedings of the Royal Society A, 463(2083), 1771-1790 (2007).
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• Analysis of rotation-vibration relative equilibria on the example of a tetrahedral four atom molecule. K. Efstathiou, D. A. Sadovskií, B. I. Zhilinskií. SIAM Journal on Applied Dynamical Systems, 3(3), 261-351 (2004).
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• Escapes and recurrence in a simple Hamiltonian system. G. Contopoulos, K. Efstathiou. Celestial Mechanics and Dynamical Astronomy, 88(2), 163-183 (2004).
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• Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields. K. Efstathiou, R. H. Cushman, D. A. Sadovskií. Physica D, 194(3-4), 250-274 (2004).
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• Global bending quantum number and the absence of monodromy in the HCN-CNH molecule. K. Efstathiou, M. Joyeux, D. A. Sadovskií. Physical Review A, 69(3), 032504 (2004).
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• 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. K. Efstathiou, D. A. Sadovskií. Nonlinearity, 17(2), 415-446 (2004).
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• Linear Hamiltonian Hopf bifurcation for point-group-invariant perturbations of the 1:1:1 resonance. K. Efstathiou, D. A. Sadovskií, R. H. Cushman. Proceedings of the Royal Society A, 459(2040), 2997-3019 (2003).
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• Orbits in the H2O molecule. K. Efstathiou, G. Contopoulos. Chaos, 11(2), 327-334 (2001).
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• A method for accurate computation of the rotation and the twist numbers of invariant circles. K. Efstathiou, N. Voglis. Physica D, 158(1-4), 151-163 (2001).
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Lecture Notes

• No polar coordinates. Lectures by R. H. Cushman. K. Efstathiou, D. A. Sadovskií. In Geometric Mechanics and Symmetry. The Peyresq Lectures, J. A. Montaldi, T. S. Ratiu eds. London Mathematical Society Lecture Note Series, 306, Cambridge University Press (2005).
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PhD Thesis

• Métamorphoses de systèmes Hamiltoniens avec symétries. K. Efstathiou. PhD thesis, Université du Littoral-Côte d'Opale, Dunkerque (2004).
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