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• Mathematical Understanding of Nature. The Mathematical Intelligencer, 2019, 10.1007/s00283-019-09932-5

• A water-based proof of the Cauchy-Schwarz inequality. American Mathematical Monthly, in press. 

• With G. Bor, Matrix Composition via Rolling Cones,  arXiv:1908.04965, Aug. 2019

• Geometrical aspects of rapid vibrations and rotations377Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Scienceshttp://doi.org/10.1098/rsta.2019.0014

• Tire Track geometry and integrable curve evolution, with G. Bor, S. Tabachnikov and R. Perline, IMRN, 2018, pp. 1-71

• Gaussian Curvature and Gyroscopes, with G. Cox, CPAM 71(5), pp. 938-952, 2018

• Bouncing in Gravitational Field, with G. Galperin, Contemp. Math. Vol. 698 (2017): Dynamical Systems, pp. 129-139

• Schroedinger's equation and bike tracks-a connection, J. Geometry and Physics, V. 115, May 2017, pp. 124-139

• Stability interchanges in a curved Sitnikov's problem, with L. Franco-Perez, M. Gidea and E. Perez-Chavela, Nonlinearity 29(2016), pp. 1056-1079

• A Coriolis force in an inertial frame. With O. Kirillov Nonlinearity 30(2017) no. 3, pp. 1109-1119

• Rotating saddle trap as Foucalt's pendulum, with O. Kirillov, Am. J. Phys., Vol. 84, No. 1, 2016

• Arnold diffusion in a pendulum lattice, with V. Kaloshin and M. Saprykina, Comm Pure Appl. Math., Vol. X17, 748-755 (2014)

• Large scale radial stability density of Hill's equation, with H. Broer and C. Simo, Nonlinearity 26(2013), 565-589

• Traveling waves in chains of pendula, with A. Saadatpour, Physica D 244 (2013), pp. 68-73

• Tractrices, bicycle tire tracks, hatchet planimeter and a 100-year old conjecture. Amer. Math Monthly 120 (2013), no. 3, pp. 199-216

• Through-the-wall detection of stationary human targets using Doppler radar, with R. M. Narayanan, M.C Shastry and P.-H. Chen. Prog. in Electromagnetics Res. B, V. 20, 147-166, 2010.

• On bicycle tire tracks geometry, hatchet planimeter, Menzin's conjecture and oscillation of unicycle tracks, Exp. Math, 18 2 (2009)

• Making the moon reverse its orbit, or stuttering in the planar three-body problem, with S. Kaplan and R. Montgomery. Discr. Cont. Dyn. Systems. Series B 10 (2008), No. 2-3, pp. 569-595

• Geometry of Arnold diffusion, with V. Kaloshin.  SIAM Review, Vol. 50 (2008), No. 4, 702-720

• An example of Arnold diffusion for near-integrable Hamiltonians, with V. Kaloshin. Bull. Amer. Math. Soc. (N.S.) 45 (2008), No. 3, pp. 409-427

• Riemann mapping theorem by steepest descent. Amer. Math. Monthly 114 (2007), No. 3, 246-251

• The Poncelet grid and billiards in ellipses, with S. Tabachnikov. Amer. Math. Monthly 114 (2007), no. 10, 895-908

• Geometry of vibrational stabilization and some applications. Int. J. Bifurcation and Chaos, Vo. 15, No. 9 (2005), 2747-2756

• Geodesics on vibrating surfaces and curvature of the normal family, with Q. Rea. Nonlinearity 18 (2005), 2737-2743

• Geometrical methods in mechanics. In MASS Selecta, S. Katok, A. Sossinsky, S. Tabachnikov, Eds., AMS, 2003. 

• On a problem by Arnold on periodic motions in magnetic fields, Comm. Pure App. Math, Vol. LVI, No. 8, pp. 1165-1177, 2003

• Non-holonomic effects and averaging, with W. Weckesser. Erg. Th. & Dynam. Sys. (2002), 22, 1497-1506

• Minimal perimeter triangles. Amer. Math. Monthly, 109, pp. 899-890, 2002

•  A Lagragian proof of the invariant curve theorem for twist mappings, with J. Moser. Proc. Symp. Pure Math., Vol. 69, 2001, pp. 733-746

• Geometry and physics of averaging, with applications. Physica D 132 (1999), pp. 150-164. 

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

• Parametically forced sine-Gordon equation and domain walls dynamics in ferromagnets. Phys. Rev. B., 57, No. 9, 1998, pp. 5033-5035

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

• Oscillatory escape in a Dyffing equation with a polynomial potential, with J. You. J. Diff. Equations, Vol. 140 No. 2 (1997), pp. 415-426

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

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

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

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

• Boundedness of solutions with quasi periodic potentials, with E. Zehnder. SIAM J. Math. Anal. Vol. 26, No. 5, pp. 1233-1256, 1995 

• 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 

• Geometric phases in the motion of rigid bodies. Arch. Rational Mech. Anal. 122(1993), pp. 213-229

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

• Invariant foliations in forced oscillations, in "Geometry and Dynamics", Broer and Takens, Eds., pp. 43-50, 1992. 

• On Littlewood's counterexample of unbounded motions in super quadratic potentials. Dynamics Reported, 1 (New Series), 113-124, 1992

• Qualitative dynamics of planar chains, with S. Laederich. Physica D 54 (1992(, pp. 173-182

• Quasiperiodic motions in superquadratic time-periodic potentials. Comm. Math. Phys. 143, pp. 43-83 (1991)

• Constrained relative motions in rotational mechanics, with J. Baillieul. Arch. Rational Mech. Anal. 115 (1991), pp. 101-135

• Geometry and computation of the dynamics of coupled pendular, with M. Henderson and F. Odeh. Int. J. Bifurcation and Chaos, Vol. 1, No. 1, 1991, pp. 27-50

• Invariant curves in time-dependent potentials, with S. Laederich. Ergod. Th. & Dynam. Sys. (1991), 11, pp. 365-378

• A period-adding phenomenon, SIAM J. App. Math. Vol. 50, No. 4, pp. 943-955, 1990

• Dynamics of discrete Frankel-Kontorova models. Analysis, et cetera. P Rabinowitz and E. Zehnder, Eds., Academic Press, inc., pp. 471-494, 1990

• KAM theory for particles in periodic potentials. Erg. Th. & Dynam. Sys., Vol. 10 (1990), pp. 777-785

• Morse theory of a model space structure. Contemp. Math. Vol. 97, pp. 209-216, 1989

• Caterpillar solutions in coupled pendula. Erg. Th. & Dynam. Sys., Vol. 8*, pp. 153-174

• Non-chaotic behavior on the Josephson Junction. Phys Rev. A, 37(3) (1988), pp. 927-931

• Stability of the inverted pendulum-a topological explanation. SIAM Review, Vol. 30 (4), 1988, pp. 639-644 

• Transversal heteroclinic intersections in slowly varying Hamiltonian systems, with H. Kurland. Dynamical systems approaches to systems and circuits, F. Salam and M. Levi, Eds., pp. 29-38, SIAM, Philadelphia, 1988

• Rotational elastic dynamics, with J. Baillieul. Physica 27D (1987), pp. 43-62

• The mechanics of rotating structures, with J. Baillieul. In Theory and Apple. of Nonlinear Control Systems, C. Byrnes, Al. Lindquist, Eds. Elsevier, pp. 497-505, 1986

• On Stability of symplectic maps. J. Diff. Eqs., Vol. 50, No. 3 (1981), pp. 441-443

• Qualitative analysis of the periodically forced relaxation oscillations. Memoirs of the AMS #244, 1981

• Adiabatic invariants of linear hamiltonian systems with periodic coefficients. J. Diff. Eq., Vol. 42, No. 1 (1981), pp. 47-71

• Dynamics of the Josephson Junction, with F. Hoppenstead and W. Miranker. Quarterly of Applied Mathematics,1978. 

 

 

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