Holger R. Dullin's List of Publications

Publications as listed in Mathematical Reviews

Preprints

[58]  S. Schmidt and H. R. Dullin. Dynamics near the p : -q Resonance

Preprint

Refereed Journal Publications

[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, and 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 and H. R. Dullin and 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, and 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, 2008.   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. (6), 17:495–517, 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 resonance.

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. Publikationen zu Wissenschaftlichen Filmen, 13, 1997. 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

August 2009