Mark Levi

Professor
Ph.D. Courant Institute, NYU
Dynamical systems and their applications in physics and engineering
Mark Levi analyzes dynamical systems arising in mechanics, electricity and other physical settings. His research aims at discovering and explaining new phenomena using geometry and analysis. He enjoys exploring and exploiting the interplay between mathematics and physics.

An outline of my research

Graduate Students

Math 251H - Fall 2008

Some publications:

A period-adding phenomenon. SIAM J. Appl. Math., Vol. 5 No. 4 (1990), pp. 943-955.

Quasiperiodic motions in superquadratic potentials. Comm. Math. Physics, 143, 43-83 (1991).

Non-chaotic behavior in the Josephson junction. Phys. Rev. A, 1988.

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

Composition of rotations and parallel transport. Nonlinearity 9 (1996) 413-419.

A "bicycle wheel" proof of the Gauss-Bonnet theorem. Expo. Math. 12(1994), 145-164.

Boundedness of solutions for quasiperiodic potentials, with E. Zehnder. SIAM J. Math. Anal. Vol. 26, No. 5 (1995), pp. 1233-1256.

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

"Geometrical aspects of stability theory for Hill's equations . with H. Broer. Arch. Rat. Mech. Anal. 131 (1995) 225-240.

A new randomness-generating mechanism in forced relaxation oscillations. (1998), Physica D 114 (1998) 230-236.

Geometry of Kapitsa's potentials, Nonlinearity 11 (1998) 1365-1368.

Curvature effects in averaging with applications, a preprint.

Parametrically forced sine-Gordon equation and domain walls dynamics in ferromagnets. With I. Mitkov and V. Zharnitsky, Phys. Rev. B Vol. 57, No. 9 (1998) 5033-5035.

A solution to Arnold's problem on the motion of charged particles in magnetic field, a preprint.