Refereed Journal Publications

[92]  M. Z. Rafat, H. R. Dullin, Boris T. Kuhlmey, Alessandro Tuniz, Haoyuan Luo, Dibyendu Roy, Sean Skinner, Tristram J. Alexander, Michael S. Wheatland, C. Martijn de Sterke. Self-stabilization of light sails by damped internal degrees of freedom.
2021. Preprint
[91]  H. R. Dullin and Robert Marangell. An Evans function for the linearised 2D Euler equations using Hill's determinant.
2021. Preprint
[90]  Nathan Duignan and H. R. Dullin. On the C8/3-regularisation of simultaneous binary collisions in the planar 4-body problem.
Nonlinearity, 34:4944–4982, 2021. Preprint
[89]  Sean Dawson and H. R. Dullin and Diana M.H. Nguyen. Monodromy in prolate spheroidal harmonics.
Studies in Applied Mathematics, 146:953–982, 2021. Preprint
[88]  Nathan Duignan and H. R. Dullin. On the C8/3-regularisation of simultaneous binary collisions in the collinear 4-body problem.
Journal of Differential Equations, 269:7975–8006, 2020. Preprint
[87]  Alain Albouy and H. R. Dullin. Relative equilibra of the 3-body problem in R4.
Journal of Geometric Mechanics, 12(3):323–341, 2020. Preprint
[86]  H. R. Dullin and Jürgen Scheurle. Symmetry reduction of the 3-body problem in R4.
Journal of Geometric Mechanics, 12(3):377–394, 2020. Preprint
[85]  H. R. Dullin, Yuri Latushkin, Robert Marangell, Shibi Vasudevan, and Joachim Worthington. Instability of unidirectional flows for the 2D α-Euler equations.
Communications on Pure and Applied Analysis, 19:2051–2079, 2020. Preprint
[84]  Jaume Alonso, H. R. Dullin, and Sonja Hohloch. Symplectic classification of coupled angular momenta.
Nonlinearity, 33:417–468, 2019. Preprint
[83]  H. R. Dullin and Joachim Worthington. Stability theory of the three-dimensional Euler equations.
SIAM J. Appl. Math., 79(5):2168–2191, 2019. Preprint
[82]  H. R. Dullin, James D. Meiss, and Joachim Worthington. Poisson structure of the three-dimensional Euler equations in Fourier space.
Journal of Physics A: Mathematical and Theoretical, 52(36):365501, 2019. Preprint
[81]  Nathan Duignan and H. R. Dullin. Regularisation for planar vector fields.
Nonlinearity, 33:106–138, 2019. Preprint
[80]  I. Chiscop and H. R. Dullin and K. Efstathiou and H. Waalkens. A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy.
Journal of Mathematical Physics, 60:032103, 2019. Preprint
[79]  J. Alonso, H. R. Dullin, and S. Hohloch. Taylor series and twisting-index invariants of coupled spin-oscillators.
Journal of Geometry and Physics, 140:131–151, 2019. Preprint
[78]  N. Martynchuk, H. R. Dullin, K. Efstathiou and H. Waalkens. Scattering invariants in Euler's two-center problem.
Nonlinearity, 32:1296–1326, 2019. Preprint
[77]  H. R. Dullin and W. Tong. Using the geometric phase to optimize planar somersaults.
IMA J. Appl. Math., 84(1):44–52, 2019. Preprint
[76]  H. R. Dullin and H. Waalkens. Defect in the joint spectrum of hydrogen due to monodromy.
Phys. Rev. Lett., 120:020507, 2018. Preprint   Editors' Suggestion
[75]  H. R. Dullin and J. Worthington. Stability results for idealised shear flows on a rectangular periodic domain.
J. Math. Fluid Mech., 20:473–484, 2018. Preprint
[74]  H. R. Dullin and W. Tong. A new twisting somersault: 513XD.
Journal of Nonlinear Science, 27:2037–2061, 2017. Preprint
[73]  H. R. Dullin, and W. Tong. Twisting somersault.
SIADS, 15:1806–1822, 2016. Preprint   Also see SIAM Nugget in SIAM News
[72]  S. Bharadwaj, N. Duignan, H. R. Dullin, K. Leung, and W. Tong. The diver with a rotor.
Indagationes Mathematicae, 27:1147–1161, 2016. Preprint
[71]  H. R. Dullin, R. Marangell, and J. Worthington. Instability of equilibria for the 2D Euler equations on the torus.
SIAP, 76:1446–1470, 2016. Preprint
[70]  H. R. Dullin and R. Montgomery. Syzygies in the two center problem
Nonlinearity, 29:1212–1237, 2016. Preprint
[69]  H. R. Dullin and A. Pelayo. Generating hyperbolic singularities in semitoric systems via Hopf bifurcations
Journal of Nonlinear Science, 26(3):787-811, 2016. Preprint
[68]  S. Arunasalam, H. R. Dullin, D. M. H. Nguyen. The Lie-Poisson structure of the symmetry reduced regularized n-body problem
Journal of Physics A: Mathematical and Theoretical, 48(6):065202, 2015. Preprint
[67]  H. R. Dullin and Joachim Worthington. The Vanishing Twist in the Restricted Three Body Problem
Physica D, 276:12–20, 2014. Preprint
[66]  D. Rose and H. R. Dullin. A symplectic integrator for the symmetry reduced and regularised planar 3-body problem with vanishing angular momentum
Celestial Mechanics and Dynamical Astronomy, 117:169–185, 2013. Preprint
[65]  G. Papadopoulos and H. R. Dullin. Semi-global Symplectic Invariants of the Euler Top
Journal of Geometric Mechanics, 5:215–232, 2013. Preprint
[64]  H. R. Dullin. The Lie-Poisson structure of the reduced n-body problem
Nonlinearity, 26:1565–1579, 2013. Preprint
[63]  H. R. Dullin. Semi-global Symplectic Invariants of the Spherical Pendulum
J. Differential Equations, 254:2942–2963, 2013. Preprint
[62]  W. Tong, H. R. Dullin. The equilateral pentagon at zero angular momentum: Maximal rotation through optimal deformation
SIAM J. Appl. Dyn. Syst., 11(3):963–987, 2012. Preprint
[61]  H. R. Dullin, H. E. Lomelí, J. D. Meiss. Symmetry reduction by lifting for maps
Nonlinearity, 25:1709–1733, 2012. Preprint
[60]  H. R. Dullin, H. Hanßmann. The degenerate C. Neumann system I: symmetry reduction and convexity
Cent. Eur. J. Math., 10:1627–1654, 2012. Preprint
[59]  H. R. Dullin, J. D. Meiss. Resonance and twist in volume-preserving mappings
SIAM J. Appl. Dyn. Syst., 11:319–349, 2012. Preprint
[58]  S. Schmidt, H. R. Dullin. Dynamics near the p : -q Resonance
Physica D, 239:1884–1891, 2010. Preprint
[57]  N. J. Fitch, C. A. Weidner, L. P. Parazzoli, H. R. Dullin, and H. J. Lewandowski.
Experimental Demonstration of Classical Hamiltonian Monodromy in the 1:1:2 Resonant Elastic Pendulum
Phys. Rev. Lett., 103:034301, 2009.   Preprint.   Also see APS Physics! - spotlight on exceptional research
[56]  H. R. Dullin, H. Waalkens. Dullin and Waalkens Reply to Comment on ``Non-uniqueness of the phase shift in central scattering due to monodromy''.
Phys. Rev. Lett., 102:188902, 2009.
[55]  S. Schmidt, H. R. Dullin, P. H. Richter. A Poincaré section for the general heavy rigid body
SIAM J. Appl. Dyn. Syst., 8:371-389, 2009. Preprint
[54]  H. R. Dullin, J. D. Meiss. Quadratic Volume Preserving Maps: Bifurcations and Invariant Circles
SIAM J. Appl. Dyn. Syst., 8:76-128, 2009. Preprint
[53]  H. R. Dullin, H. Waalkens. Non-uniqueness of the phase shift in central scattering due to monodromy.
Phys. Rev. Lett., 101:070405, 2008.
[52]  H. R. Dullin, J. D. Meiss. Nilpotent normal form for divergence-free vector fields and volume-preserving maps
Physica D, 237:156–166, 2007.   Preprint
[51] R. Cushman, H.R. Dullin, H. Hanßmann, S. Schmidt The 1:\pm 2 resonance
Regul. Chaotic Dyn., 12:642–663, 2007.   Preprint
[50] H.R. Dullin, Vu Ngoc S. Symplectic Invariants near Hyperbolic-Hyperbolic Points
Regul. Chaotic Dyn., 12:689–716, 2007.   Preprint
[49] H.R. Dullin, A. Tsygvintsev. On the analytic non-integrability of the Rattleback problem
Ann. Fac. Sci. Toulouse Math., 17(3):495–517, 2008. Preprint
[48] C.M. Davison, H.R. Dullin. Geodesic flow on three dimensional ellipsoids with equal semi-axes
Regul. Chaotic Dyn., 12:172–197, 2007.   Preprint
[47] C.M. Davison, H.R. Dullin, A.V. Bolsinov. Geodesics on the Ellipsoid and Monodromy
J. Geom. Phys., 57:2437–2454, 2007.   Preprint
[46] H. R. Dullin, S. Schmidt, P. H. Richter, and S. Großmann. Extended Phase Diagram of the Lorenz Model.
Int. J. Bif. Chaos, 17:3013–3033, 2007.   Preprint
[45] A. V. Bolsinov, H. R. Dullin, and A. P. Veselov. Spectra of Sol-manifolds: Arithmetic and Quantum Monodromy.
Comm. Math. Phys., 264:583–611, 2006.   Preprint
[44] H. R. Dullin, A. V. Ivanov, and J. D. Meiss. Normal Forms for Symplectic Maps with Twist Singularities.
Physica D, 215:157–190, 2006.   Preprint
[43]  H. R. Dullin and A.V. Ivanov. Another look at the saddle-centre bifurcation: Vanishing Twist
Physica D, 211:47–56, 2005.   Preprint
[42]  H. R. Dullin, J. Robinson, H. Waalkens, S. Creagh, and G. Tanner. Maslov indices and monodromy.
J. Phys. A, 38:L443–L447, 2005.   Preprint
[41]  H. R. Dullin, J. D. Meiss and D. G. Sterling. Symbolic Codes for Rotational Orbits.
SIADS, 4:515–562, 2005.   Preprint
[40]  H. R. Dullin and A.V. Ivanov. Vanishing twist in the Hamiltonian Hopf bifurcation.
Physica D, 201:27–44, 2005.   Preprint
[39]  H. R. Dullin. Poisson Integrator for Symmetric Tops.
Regular and Chaotic Dynamics, 9:255–264, 2004.   Preprint
[38]  H. R. Dullin and V. Matveev. A new integrable system on the sphere.
Math Research Letters, 11:715–722, 2004. Preprint
[37]  R. H. Cushman, H. R. Dullin, A. Giacobbe, D. D. Holm, M. Joyeux, P. Lynch, D. A. Sadovskii, and B. I. Zhilinskii.
The CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy.
Phys. Rev. Lett., 93:24302, 2004.   Also see I. Stewart. Quantizing the classical cat, Nature 430:731-732, 2004.
[36]  H. Waalkens, P. H. Richter, and H. R. Dullin. The problem of two fixed centers: bifurcations, actions, monodromy.
Physica D, 196:265–310, 2004.   Preprint
[35]  H. R. Dullin, and Vu Ngoc San. Vanishing Twist near Focus-Focus points.
Nonlinearity, 17:1777–1786, 2004.   Preprint
[34]  H. R. Dullin, and F. Fasso. An algorithm for detecting Directional Quasi-Convexity.
BIT Numerical Analysis, 44:571–584, 2004.   Preprint
[33]  H. R. Dullin, G. Gottwald, and D. D. Holm. On asymptotically equivalent shallow water wave equations.
Physica D, 190:1–14, 2004.   Preprint
[32]  H. R. Dullin, A. Giacobbe, and R. Cushman. Monodromy in the resonant swing spring.
Physica D, 190:15–37, 2004.   Preprint
[31]  H. R. Dullin, G. Gottwald, and D. D. Holm.
Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves.
Fluid Dynamics Research, 33:73–95, 2003.   Preprint
[30]  H. Waalkens, A. Junge, and H. R. Dullin. Quantum Monodromy in the two-centre problem.
J. Phys. A, 36:L307–L314, 2003.   Preprint
[29]  H. R. Dullin, and J. D. Meiss. Twist Singularities for Symplectic Maps.
Chaos, 13:1–16, 2003.   Preprint (5.6 MB)
[28]  H. R. Dullin, J. E. Howard, and M. Horányi. Generalizations of the Störmer problem for dust grain orbits.
Physica D, 171:178–195, 2002.   Preprint
[27]  H. Waalkens and H. R. Dullin. Quantum monodromy in prolate ellipsoidal billiards.
Ann. Physics, 295:81–112, 2002.   Preprint
[26]  H. R. Dullin, G. Gottwald, and D. D. Holm. An integrable shallow water equation with linear and nonlinear dispersion.
Phys. Rev. Lett., 87:4501, 2001.   Preprint
[25]  H. R. Dullin and A. Bäcker. About ergodicity in the family of limaçon billiards.
Nonlinearity, 14:1673–1687, 2001.   Preprint
[24]  H. R. Dullin, P. H. Richter, A. P. Veselov, and H. Waalkens. Actions of the Neumann system via Picard-Fuchs equations.
Physica D, 155:159–183 2001.   Preprint
[23]  H. R. Dullin, D. G. Sterling, and J. D. Meiss. Self-rotation number for maps of the plane.
Physica D, 145:25–46, 2000.   Preprint
[22]  H. R. Dullin and J. D. Meiss. Generalized Hénon maps: the cubic diffeomorphisms of the plane.
Physica D, 143:262–289, 2000.   Preprint
[21]  J. E. Howard, H. R. Dullin, and M. Horányi. Stability of halo orbits.
Phys. Rev. Lett., 84:3244, 2000. Preprint   Also see Nature Science Update and AIP Physics News Update .
[20]  H. R. Dullin, J. D. Meiss, and D. G. Sterling. Generic twistless bifurcations.
Nonlinearity, 13:203–224, 2000.   Preprint
[19]  D. G. Sterling, H. R. Dullin, and J. D. Meiss. Homoclinic bifurcations for the Hénon map.
Physica D, 134:153–184, 1999.   Preprint
[18]  H. R. Dullin, V. Matveev, and P. Topalov. On integrals of third degree in momenta.
Regular and Chaotic Dynamics, 4(3): 35–44, 1999.   Preprint
[17]  H. Waalkens, J. Wiersig, and H. R. Dullin. Triaxial ellipsoidal quantum billiards.
Ann. Physics, 276:64–110, 1999.   Preprint
[16]  H. R. Dullin and R. W. Easton. Stability of Levitrons.
Physica D, 126:1–17, 1999.   Preprint
[15]  H. R. Dullin, P. H. Richter, and A. P. Veselov. Action variables of the Kovalevskaya top.
Regular and Chaotic Dynamics, 3(3):18–26, 1998.   Preprint
[14]  H. R. Dullin and J. D. Meiss. Stability of minimal periodic orbits.
Phys. Lett. A, 247:227–234, 1998.   Preprint
[13]  J. E. Howard and H. R. Dullin. Linear stability of natural symplectic maps.
Phys. Lett. A, 246:273–283, 1998.   Preprint
[12]  H. R. Dullin. Symbolic dynamics and the discrete variational principle.
J. Phys. A, 31:9065–9072, 1998.   Preprint
[11]  H. R. Dullin. Linear stability in billiards with potential.
Nonlinearity, 11:151–173, 1998.   Preprint
[10]  H. Waalkens, J. Wiersig, and H. R. Dullin. Elliptic quantum billiard.
Ann. Physics, 260:50–90, 1997.   Preprint
[9]  A. V. Bolsinov and H. R. Dullin. On the Euler case in rigid body dynamics and the Jacobi problem (Russian).
Regular und Chaotic Dynamics, 2(1):13–25, 1997.
[8]  A. Bäcker and H. R. Dullin. Symbolic dynamics and periodic orbits for the cardioid billiard.
J. Phys. A, 30:1991–2020, 1997.   Preprint
[7]  P. H. Richter, H. R. Dullin, H. Waalkens, and J. Wiersig. Spherical pendulum, actions and spin.
J. Phys. Chem., 100:19124–19135, 1996.   Preprint (1.7 MB)
[6]  A. Bolsinov, H. R. Dullin, and A. Wittek. Topology of energy surfaces and existence of transversal Poincaré sections.
J. Phys. A, 29:4977–4985, 1996.   Preprint
[5]  H. R. Dullin, P. H. Richter, and A. Wittek. A two parameter study of the extent of chaos in a billiard system.
Chaos, 6:43– 58, 1996.   Preprint Figures (2.2 MB)
[4]  H. R. Dullin and A. Wittek. Complete Poincaré sections and tangent sets.
J. Phys. A, 28:7157–7180, 1995.   Preprint (1.8 MB)
[3]  H. R. Dullin, M. Juhnke, and P. H. Richter. Action integrals and energy surfaces of the Kovalevskaya top.
Bifurcation and Chaos, 4:1535–1562, 1994.   Preprint   Figures are on my Kowalevskaya page
[2]  H. R. Dullin and A. Wittek. Efficient calculation of actions.
J. Phys. A, 27:7461–7474, 1994.   Preprint
[1]  H. R. Dullin. Melnikov's method applied to the double pendulum.
Z. Phys. B, 93:521–528, 1994.   Preprint

Other Publications

H. R. Dullin and A. V. Ivanov. Twistless tori near low order ersonance.
Zapiski Nachnykh Seminarov POMI, 300:135–144, 2003. V.F. Lazutkin. Workshop on Differential Equations, St. Petersburg 2002. Journal of Mathematical Sciences, 128:2754–2760, 2005.
H. R. Dullin and R. W. Easton. Stability of Levitrons.
Z. Angew. Math. Mech., 79:S167–S170, 1999.   Preprint
H. R. Dullin. The energy surfaces of the Kovalevskaya top.
In A. Delshams and C. Simo, editors, Hamiltonian Systems with Three Degrees of Freedom, Sagaro, Spain 1995, pp 330–334. Kluwer, 1998.   Preprint
P. H. Richter, H. R. Dullin, and A. Wittek. The Kovalevskaya Top.
Film C1961 (movie). Publikationen zu Wissenschaftlichen Filmen, 13:33-96, 1997 (booklet). Institut für den Wissenschaftlichen Film (IWF), Göttingen.
P. H. Richter, H. R. Dullin, and H.-O. Peitgen. Der Spiegel, das Chaos und die Wahrheit.
Phys. Bl., 50(4):355–358, 1994.
P. H. Richter and H. R. Dullin. Der Goldene Schnitt in der Blattstellung.
In A. Deutsch, editor, Muster des Lebendigen, pp 55–70. Vieweg, 1994.   Preprint
H. R. Dullin. Die Energieflächen des Kowalewskaja-Kreisels.
Verlag Mainz, Wissenschaftsverlag, Aachen, 1994. vi+171 pp. ISBN: 3-930911-07-8 MR 97f:70009   Figures are on my Kowalevskaya page
HRD

Professor of Applied Mathematics
School of Mathematics and Statistics
University of Sydney NSW 2006
Australia

holger.dullin@sydney.edu.au
Phone: +61 2 9351 4083
FAX: +61 2 9351 4534
Office: 714 Carslaw F07

Publications

Current Teaching

MATH1902 Linear Algebra (Adv.)
MATH3977 Lagrangian and Hamiltonian Dynamics