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Research Output 1978 2019

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Article
2018
1 Citation (Scopus)

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

Gyroscope
Total curvature
Gyroscopes
Charge
Magnetic Force
2017
3 Citations (Scopus)

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

Coriolis force
Coriolis Force
hodographs
saddles
Saddle
1 Citation (Scopus)

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

Curve of pursuit
Schrödinger Equation
2016
11 Citations (Scopus)

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

saddles
pendulums
traps
stabilization
precession
3 Citations (Scopus)

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

Interchanges
Circle
Equilibrium Point
N-body Problem
ellipses
2014
6 Citations (Scopus)

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

Pendulum
Pendulums
Trajectories
Energy
Weak Coupling
2013
5 Citations (Scopus)

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

Hill Equation
Morse Function
Fine Structure
fine structure
11 Citations (Scopus)

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

Tire
Monodromy
Wheel
Motion
Circle
4 Citations (Scopus)

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

coupling coefficients
traveling waves
Josephson junctions
damping
2010
1 Citation (Scopus)

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

Twist
Theorem
Celestial Mechanics
KAM Theory
N-body Problem
36 Citations (Scopus)

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

Doppler radar
Radar systems
signatures
National security
Law enforcement
2009
11 Citations (Scopus)
Tire
Wheel
Oscillation
Monodromy
Circle
2008
20 Citations (Scopus)

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

Arnold Diffusion
Hamiltonians
Refraction
Periodic Potential
Mechanical Systems
2 Citations (Scopus)

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

Three-body Problem
Moon
Sun
Reverse
Orbits
2007

Riemann mapping theorem by steepest descent

Levi, M., Mar 1 2007, In : American Mathematical Monthly. 114, 3, p. 246-251 6 p.

Research output: Contribution to journalArticle

Steepest Descent
Theorem
18 Citations (Scopus)

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

Billiards
Grid
2005
4 Citations (Scopus)

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

Normal Family
Geodesic
Curvature
curvature
differential geometry
6 Citations (Scopus)
Pendulum
Pendulums
Stabilization
Geometry
Curve of pursuit
2003
4 Citations (Scopus)

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

Periodic Motion
Magnetic Field
Magnetic fields
2002
2 Citations (Scopus)

Minimal perimeter triangles

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

Research output: Contribution to journalArticle

Perimeter
Triangle
3 Citations (Scopus)

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

Singular Limit
Nonholonomic Systems
Planimeters
Holonomy
Acoustic waves
1999
31 Citations (Scopus)

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

curvature
physics
pendulums
geometry
traps
1998
2 Citations (Scopus)

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

relaxation oscillators
strange attractors
oscillations
19 Citations (Scopus)

Geometry of Kapitsa's potentials

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

Research output: Contribution to journalArticle

Centrifugal Force
centrifugal force
Effective Potential
Averaging
Vibration
1997
11 Citations (Scopus)

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

Hamiltonians
Duffing Equation
Polynomials
Polynomial
Discontinuity
11 Citations (Scopus)

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

Shadowing Property
Geodesic Flow
Geodesic
Torus
High-dimensional
1996
7 Citations (Scopus)

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

linear equations
coefficients
matrices
Chemical analysis
algebra
1995
60 Citations (Scopus)

Geometrical aspects of stability theory for Hill's equations

Broer, H. & Levi, M., Sep 1 1995, In : Archive for Rational Mechanics and Analysis. 131, 3, p. 225-240 16 p.

Research output: Contribution to journalArticle

Hill Equation
Stability Theory
1993
34 Citations (Scopus)

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

Geometric Phase
Rigid Body
Berry Phase
Motion
Stokes' theorem

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

Rotating
Paradox
Verify
Design
1992
1 Citation (Scopus)

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

configurations
Coriolis effect
metal spinning
integers
equations of motion
1991
28 Citations (Scopus)

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

Mechanics
Rotating
Motion
Linearization
Mechanical Systems
115 Citations (Scopus)

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

Quasi-periodic Motion
Periodic Potential
Exponential Polynomial
Motion
Singular Integrals
1990
26 Citations (Scopus)

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

KAM Theory
Periodic Potential
Lebesgue Measure
Energy
Form
24 Citations (Scopus)

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

Circle Map
Periodic Forcing
Type Systems
Experiments
Experiment
1988
32 Citations (Scopus)

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

thermometers
Josephson junctions
electric potential
37 Citations (Scopus)

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

Inverted Pendulum
Pendulum
Pendulums
Vertical
Open interval
1987
69 Citations (Scopus)

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

weightlessness
elastic properties
energy dissipation
1983
1 Citation (Scopus)

On stability of symplectic maps

Levi, M., Jan 1 1983, In : Journal of Differential Equations. 50, 3, p. 441-443 3 p.

Research output: Contribution to journalArticle

1981
5 Citations (Scopus)

Adiabatic invariants of the linear Hamiltonian systems with periodic coefficients

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

Research output: Contribution to journalArticle

Adiabatic Invariant
Periodic Coefficients
Hamiltonian Systems
Linear Systems
1978
90 Citations (Scopus)

DYNAMICS OF THE JOSEPHSON JUNCTION.

Levi, M., Hoppensteadt, F. C. & Miranker, W. L., Jan 1 1978, In : Quarterly of Applied Mathematics. 36, 2, p. 167-198 32 p.

Research output: Contribution to journalArticle

Josephson Junction
sine-Gordon equation
Sine-Gordon Equation
Discrete Approximation
Periodic Solution