Publications:

[1] Stability of Linear Hamiltonian Systems With Periodic Coefficients. IBM Research Report, 1977.

[2] With F.C. Hoppensteadt, W.L. Miranker, Dynamics of the Josephson Junction, Quarterly of Applied Mathematics, July 1978.

[3] Relaxation Oscillations With Periodic Forcing, Proc. Conf. on Dynamical Systems at Northwestern, June 1979.

[4] Adiabatic Invariants of Linear Hamiltonian Systems. In Classical Mechanics and Dynamical Systems, R. Devaney and Z. Nitecki, Eds. Marcel Dekker, Inc. New York and Basel, 1981, pp. 123-124.

[5] Adiabatic Invariants of Linear Hamiltonian Systems with Periodic Coefficients, J.~Diff. Eq., V.42, No.1(1981), P.47-71.

[6] Qualitative Analysis of the Periodically Forced Relaxation Oscillations, Mem. AMS \#244, 1981.

[7] Random Behavior in Deterministic Systems, Proceedings of Joint Automatic Control Conference, University of Virginia, Charlottesville, 1981.

[8] On Stability of Symplectic Maps, J. Diff. Eq., Vol.50 No.3(1981), pp.441- 443.

[9] With J. Baillieul, Dynamics of Rotating Flexible Space Structures, in Proc. of the CDC IEEE Conf., San Antonio, TX, 1983.

[10] Soviet Research on Dynamical Systems, in "Report on Soviet Applied Mathematics", Science Applications, Inc., McLean, VA, 1984.

[11] A Note on the Minimal Polyhedra Circumscribed Around a Convex Body, MSRI 059- 84-5 (1984).

[12] Beating Modes in the Josephson Junction in "Chaos in Nonlinear Systems", J.~Chandra, Ed., SIAM, Philadelphia, 1984.

[13] With J. Baillieul, The Mechanics of Rotating Structures, in Theory and Appl. of Nonlinear Control Systems, C. Byrnes, A. Lindquist, Ed., Elsevier, pp. 497--505, 1986.

[14] With J. Baillieul, Rotational elastic dynamics, Physica 27D(1987) 43--62.

[15] with H. Kurland, Transversal Heteroclinic Intersections in Slowly Varying Hamiltonian Systems, in Dynamical Systems Approaches to Nonlinear Problems in Systems and Circuits, F. Salam and M. Levi, eds., pp. 29--38, SIAM, Philadelphia, 1988.

[16] Stability of the Inverted Pendulum -- a Topological Explanation. SIAM Review, v.30(4), 1988, pp. 639--644.

[17] Non-chaotic Behavior in the Josephson Junction, Phys. Rev. A, 37(3) (1988), pp. 927--931.

[18] Caterpillar Solutions in Coupled Pendula, Erg. Th.\& Dyn. Sys., $8 *$(1988) (C.C.~Conley memorial issue), pp. 153--174.

[19] Morse Theory of a Model Space Structure, Contemp. Math. vol. 97, pp. 209--216, 1989.

[20] KAM theory for particles in periodic potentials, Erg. Th.\& Dyn. Sys., Vol. 10 (1990), 777-785.

[21] Dynamics of discrete Frenkel--Kontorova Models. Analysis, et cetera, (A collection of papers dedicated to J. Moser's 60th birthday). P. Rabinowitz and E. Zehnder, Eds., Academic Press, Inc., pp. 471--494, 1990.

[22] A Period--adding phenomenon, SIAM J. Appl. Math. Vol. 50, No. 4, pp. 943--955, June 1990.

[23] With S. Laederich, Invariant curves in time--dependent potentials, Ergod. Th. \& Dynam. Sys. (1991), 11, 365-378.

[24] With M. Henderson and F. Odeh, Geometry and computation of the dynamics of coupled pendula, Int. J. Bifurcation and Chaos, Vol. 1, No. 1, 1991, 27--50.

[25] With J. Baillieul, Constrained relative motions in rotational mechanics, Arch. Rational Mech. Anal. 115 (1991) 101--135.

[26] Quasiperiodic motions in superquadratic time--periodic potentials. Comm. Math. Phys. 143, 43--83 (1991).

[27] With S.Laederich, Qualitative dynamics of planar chains, Physica D 54 (1992) 173--182.

[28] On Littlewood's counterexample of unbounded motions in superquadratic potentials. Dynamics Reported, 1 (New Series), 113--124, 1992.

[29] Invariant foliations in forced oscillations, in "Geometry and Dynamics, Broer and Takens, Eds. pp. 43--40, 1992.

[30] Gyroscopic effects in a rotating sleeve hydrocyclone. Appl. Math. Lett. Vol. 6, No. 4, pp. 91--95, 1993.

[31] A theorem of Poinsot, path ordered integrals and parallel transport. Fields Institute Communications, Vol. 1, pp. 133--138 (1993).

[32] Geometric Phases in the Motion of Rigid Bodies, Arch. Rational Mech. Anal. 122(1993) 213--229.

[33] A ``bicycle wheel'' proof of the Gauss--Bonnet theorem, dual cones and some mechanical manifestations of the Berry phase. Expo. Math. 12(1994), pp. 145-164.

[34] Boundedness of solutions with quasiperiodic potentials, with E. Zehnder, SIAM J. Math. Anal. Vol. 26, No. 5, pp. 1233-1256, 1995.

[35] Geometric aspects of stability for Hill's equations, with H. Broer. Arch. Rational Mech. Anal. 131(1995) 225-240.

[36] Geometry of stabilization by vibration, with W. Weckesser, SIAM Review Vol. 37, No. 2, pp. 219-223, 1995.

[37] Composition of Rotations and Parallel Transport, Nonlinearity 9 (1996), 413-419.

[38] Shadowing property of geodesics in the Hedlund's metric, Ergod.Th. \& Dynam. Sys. (1997), 17, 187-203

[39] A new randomness--generating mechanism in forced relaxation oscillations. Physica D, to appear.

[40] With J. You, Oscillatory escape in a Duffing equation with a polynomial potential. J. Diff. Equations, {\bf 139} (1997).


Preprints:

[41] With I. Mitkov and V. Zharnitsky, Parametrically forced sine-Gordon equation and domain walls dynamics in ferromagnets. Phys. Rev. A.

[42] Geometry of Kapitsa's potentials, Nonlinearity

[43] Curvature Effects in Averaging With Applications.

[44] Geometry in upside-down pendula, Paul traps and laser tweezers.

[45] On the geometry and physics of high-frequency vibrations.

[46] Dripping Faucets, Torus Flows and Morse-Thue sequences.

[47] On non--exact area--preserving maps.

[48] Universality in forced relaxation oscillations, a preprint.

[49] A solution to Arnold's problem of periodic motions in magnetic fields.


Back to Mark Levi's Home Page Back to research outline