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Research Output

2020

A Water-Based Proof of the Cauchy–Schwarz Inequality

Levi, M., Jul 2 2020, In : American Mathematical Monthly. 127, 6, 1 p.

Research output: Contribution to journalComment/debate

Hill's equation, tire tracks and rolling cones

Bor, G. & Levi, M., Apr 1 2020, In : Nonlinearity. 33, 4, p. 1424-1442 19 p.

Research output: Contribution to journalArticle

The ponderomotive Lorentz force

Cox, G. & Levi, M., Aug 2020, In : Nonlinearity. 33, 8, p. 4030-4045 16 p.

Research output: Contribution to journalReview article

2019
2018

Gaussian Curvature and Gyroscopes

Cox, G. & Levi, M., May 2018, In : Communications on Pure and Applied Mathematics. 71, 5, p. 938-952 15 p.

Research output: Contribution to journalArticle

2 Scopus citations
2017

A Coriolis force in an inertial frame

Kirillov, O. & Levi, M., Feb 3 2017, In : Nonlinearity. 30, 3, p. 1109-1119 11 p.

Research output: Contribution to journalArticle

4 Scopus citations

Bouncing in gravitational field

Galperin, G. & Levi, M., Jan 1 2017, Contemporary Mathematics. American Mathematical Society, p. 129-139 11 p. (Contemporary Mathematics; vol. 698).

Research output: Chapter in Book/Report/Conference proceedingChapter

Schrödinger's equation and “bike tracks” — A connection

Levi, M., May 1 2017, In : Journal of Geometry and Physics. 115, p. 124-130 7 p.

Research output: Contribution to journalArticle

1 Scopus citations
2016

Rotating saddle trap as Foucault's pendulum

Kirillov, O. N. & Levi, M., Jan 1 2016, In : American Journal of Physics. 84, 1, p. 26-31 6 p.

Research output: Contribution to journalArticle

13 Scopus citations

Stability interchanges in a curved Sitnikov problem

Franco-Pérez, L., Gidea, M., Levi, M. & Pérez-Chavela, E., Feb 12 2016, In : Nonlinearity. 29, 3, p. 1056-1079 24 p., 1056.

Research output: Contribution to journalArticle

4 Scopus citations
2015

Alphabet size selection for symbolization of dynamic data-driven systems: An information-theoretic approach

Sarkar, S., Chattopdhyay, P., Ray, A., Phoha, S. & Levi, M., Jul 28 2015, ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., Vol. 2015-July. p. 5194-5199 6 p. 7172150

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations
2014

Arnol'd diffusion in a pendulum lattice

Kaloshin, V., Levi, M. & Saprykina, M., May 1 2014, In : Communications on Pure and Applied Mathematics. 67, 5, p. 748-775 28 p.

Research output: Contribution to journalArticle

6 Scopus citations
2013

Large scale radial stability density of Hill's equation

Broer, H., Levi, M. & Simo, C., Feb 1 2013, In : Nonlinearity. 26, 2, p. 565-589 25 p.

Research output: Contribution to journalArticle

5 Scopus citations

Tractrices, bicycle tire tracks, hatchet planimeters, and a 100-year-old conjecture

Foote, R., Levi, M. & Tabachnikov, S., Mar 1 2013, In : American Mathematical Monthly. 120, 3, p. 199-216 18 p.

Research output: Contribution to journalArticle

12 Scopus citations

Traveling waves in chains of pendula

Saadatpour, A. & Levi, M., Feb 1 2013, In : Physica D: Nonlinear Phenomena. 244, 1, p. 68-73 6 p.

Research output: Contribution to journalArticle

4 Scopus citations
2010

Some applications of moser's twist theorem

Levi, M., Sep 29 2010, In : Handbook of Dynamical Systems. 3, C, p. 225-247 23 p.

Research output: Contribution to journalArticle

1 Scopus citations

Through-the-wall detection of stationary human targets using doppler radar

Narayanan, R. M., Shastry, M. C., Chen, P. H. & Levi, M., Jan 1 2010, In : Progress In Electromagnetics Research B. 20, p. 147-166 20 p.

Research output: Contribution to journalArticle

38 Scopus citations
2009
11 Scopus citations
2008

An example of Arnold diffusion for near-integrable Hamiltonians

Kaloshin, V. & Levi, M., Jul 2008, In : Bulletin of the American Mathematical Society. 45, 3, p. 409-427 19 p.

Research output: Contribution to journalArticle

20 Scopus citations

Geometry of Arnold diffusion

Kaloshin, V. & Levi, M., Nov 24 2008, In : SIAM Review. 50, 4, p. 702-720 19 p.

Research output: Contribution to journalReview article

21 Scopus citations

Making the moon reverse its orbit, or, stuttering in the planar three-body problem

Kaplan, S. R., Levi, M. & Montgomery, R., Dec 1 2008, In : Discrete and Continuous Dynamical Systems - Series B. 10, 2-3, p. 569-595 27 p.

Research output: Contribution to journalArticle

2 Scopus citations
2007

Riemann mapping theorem by steepest descent

Levi, M., Mar 2007, In : American Mathematical Monthly. 114, 3, p. 246-251 6 p.

Research output: Contribution to journalArticle

The poncelet grid and Billiards in Ellipses

Levi, M. & Tabachnikov, S., Dec 2007, In : American Mathematical Monthly. 114, 10, p. 895-908 14 p.

Research output: Contribution to journalArticle

20 Scopus citations
2005

Geodesics on vibrating surfaces and curvature of the normal family

Levi, M. & Ren, Q., Nov 1 2005, In : Nonlinearity. 18, 6, p. 2737-2743 7 p.

Research output: Contribution to journalArticle

4 Scopus citations
6 Scopus citations
2003

On a Problem by Arnold on Periodic Motions in Magnetic Fields

Levi, M., Aug 1 2003, In : Communications on Pure and Applied Mathematics. 56, 8, p. 1165-1177 13 p.

Research output: Contribution to journalArticle

4 Scopus citations
2002

Minimal perimeter triangles

Levi, M., Dec 2002, In : American Mathematical Monthly. 109, 10, p. 890-899 10 p.

Research output: Contribution to journalArticle

2 Scopus citations

Non-holonomic systems as singular limits for rapid oscillations

Levi, M. & Weckesser, W., Oct 1 2002, In : Ergodic Theory and Dynamical Systems. 22, 5, p. 1497-1506 10 p.

Research output: Contribution to journalArticle

3 Scopus citations
1999

Geometry and physics of averaging with applications

Levi, M., Jul 15 1999, In : Physica D: Nonlinear Phenomena. 132, 1-2, p. 150-164 15 p.

Research output: Contribution to journalArticle

31 Scopus citations
1998

A new randomness-generating mechanism in forced relaxation oscillations

Levi, M., Jan 1 1998, In : Physica D: Nonlinear Phenomena. 114, 3-4, p. 230-236 7 p.

Research output: Contribution to journalArticle

2 Scopus citations

Geometry of Kapitsa's potentials

Levi, M., Sep 1 1998, In : Nonlinearity. 11, 5, p. 1365-1368 4 p.

Research output: Contribution to journalArticle

19 Scopus citations
1997

Oscillatory Escape in a Duffing Equation with a Polynomial Potential

Levi, M. & You, J., Nov 1 1997, In : Journal of Differential Equations. 140, 2, p. 415-426 12 p.

Research output: Contribution to journalArticle

11 Scopus citations

Shadowing property of geodesics in Hedlund's metric

Levi, M., Feb 1997, In : Ergodic Theory and Dynamical Systems. 17, 1, p. 187-203 17 p.

Research output: Contribution to journalArticle

11 Scopus citations
1996

Composition of rotations and parallel transport

Levi, M., Dec 1 1996, In : Nonlinearity. 9, 2, p. 413-419 7 p.

Research output: Contribution to journalArticle

8 Scopus citations
1995

Geometrical aspects of stability theory for Hill's equations

Broer, H. & Levi, M., Sep 1995, In : Archive for Rational Mechanics and Analysis. 131, 3, p. 225-240 16 p.

Research output: Contribution to journalArticle

60 Scopus citations
1993

Geometric phases in the motion of rigid bodies

Levi, M., Sep 1 1993, In : Archive for Rational Mechanics and Analysis. 122, 3, p. 213-229 17 p.

Research output: Contribution to journalArticle

35 Scopus citations

Gyroscopic effects in a rotating sleeve hydrocyclone

Levi, M., Jul 1993, In : Applied Mathematics Letters. 6, 4, p. 91-95 5 p.

Research output: Contribution to journalArticle

1992

Qualitative dynamics of planar chains

Laederich, S. & Levi, M., Jan 1 1992, In : Physica D: Nonlinear Phenomena. 54, 3, p. 173-182 10 p.

Research output: Contribution to journalArticle

1 Scopus citations
1991

Constrained relative motions in rotational mechanics

Baillieul, J. & Levi, M., Jun 1991, In : Archive for Rational Mechanics and Analysis. 115, 2, p. 101-135 35 p.

Research output: Contribution to journalArticle

28 Scopus citations

Quasiperiodic motions in superquadratic time-periodic potentials

Levi, M., Dec 1 1991, In : Communications In Mathematical Physics. 143, 1, p. 43-83 41 p.

Research output: Contribution to journalArticle

116 Scopus citations
1990

KAM theory for particles in periodic potentials

Levi, M., Jan 1 1990, In : Ergodic Theory and Dynamical Systems. 10, 4, p. 777-785 9 p.

Research output: Contribution to journalArticle

26 Scopus citations

Period-adding phenomenon

Levi, M., Jan 1 1990, In : SIAM Journal on Applied Mathematics. 50, 4, p. 943-955 13 p.

Research output: Contribution to journalArticle

24 Scopus citations
1988

Nonchaotic behavior in the Josephson junction

Levi, M., Jan 1 1988, In : Physical Review A. 37, 3, p. 927-931 5 p.

Research output: Contribution to journalArticle

31 Scopus citations

Stability of the inverted pendulum - a topological explanation

Levi, M., Jan 1 1988, In : SIAM Review. 30, 4, p. 639-644 6 p.

Research output: Contribution to journalArticle

37 Scopus citations
1987

Rotational elastic dynamics

Baillieul, J. & Levi, M., Jul 1987, In : Physica D: Nonlinear Phenomena. 27, 1-2, p. 43-62 20 p.

Research output: Contribution to journalArticle

70 Scopus citations

ROTATIONAL MECHANICS OF A SIMPLE ELASTIC STRUCTURE.

Baillieul, J. & Levi, M., 1987, IFAC Proceedings Series. Rauch, H. E. (ed.). 3 ed. Pergamon Press, p. 155-160 6 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1986

MECHANICS OF ROTATING STRUCTURES.

Baillieul, J. & Levi, M., Dec 1 1986, Unknown Host Publication Title. North-Holland, p. 497-505 9 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1983

DYNAMICS OF ROTATING FLEXIBLE STRUCTURES.

Baillieul, J. & Levi, M., Dec 1 1983, In : Proceedings of the IEEE Conference on Decision and Control. 2, p. 808-813 6 p.

Research output: Contribution to journalConference article

4 Scopus citations

On stability of symplectic maps

Levi, M., Dec 1983, In : Journal of Differential Equations. 50, 3, p. 441-443 3 p.

Research output: Contribution to journalArticle

1 Scopus citations
1981

Adiabatic invariants of the linear Hamiltonian systems with periodic coefficients

Levi, M., Oct 1981, In : Journal of Differential Equations. 42, 1, p. 47-71 25 p.

Research output: Contribution to journalArticle

5 Scopus citations