Vadim Kaloshin The Michael Brin
Chair in Mathematics University of Maryland at College Park,3111 Math.
Building, College Park,MD 20740 ph:(301)
4055132 Email: vadim.kaloshin@gmail.com 




Education:


Recent Teaching:


Research Interests:o Smooth and Hamiltonian dynamics, Arnold diffusion, celestial mechanics o Growth of Sobolev norms for Hamiltonian PDEs o Billiards and spectral rigidity 

Recent Research (past few years):
Stochastic Arnold diffusiono `` Random Iteration of Maps on a Cylinder and diffusive behavior'', with O. Castejon, arXiv:115917, 2015, 75pp, [PDF]
o `` A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems'', with M. Guardia, J. Zhang , arXiv, 2015, 50pp, [PDF]
o `` Normally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances'', with J. Zhang, K. Zhang , preprint, 85pp, 2015, [PDF]
Arnold diffusion in several degrees of freedomo `` Arnold diffusion in arbitrary degrees of freedom and 3dimensional normally hyperbolic invariant cylinders'', with P. Bernard and K. Zhang, arXiv:1112.2773 [math.DS] 2011, 58pp, cond. accepted to Acta Mathematica, [PDF]
o ``Generic fast diffusion for a class of nonconvex Hamiltonians with two degrees of freedom'', with A. Bounemoura, Moscow Mathematical Journal, vol. 14, 2, 181203, 2014, [PDF]
o `` A strong form of Arnold diffusion for two and a half degrees of freedom'', with K. Zhang, arXiv:1212.1150, preprint, 2012, 207pp, [PDF]
o ``Announcement: A strong form of Arnold diffusion for two and a half degrees of freedom'', with K. Zhang, Nonlinearity, 28, no. 8, 26992720, [PDF]
o ``A strong form of Arnold diffusion for three and a half degrees of freedom'', with K. Zhang, preprint, 2014, 36pp, [PDF]
o `` Dynamics of the dominant Hamiltonian, with applications to Arnold diffusion'', with K. Zhang, arXiv:1410.1844, preprint, 2014, 84pp, [PDF]
o ``Orbits of nearly integrable tori accumulating to KAM tori'', with M. Guardia, arXiv:1412.7088, preprint, 2014, 115pp, [PDF]
o ``A note on microinstability for Hamiltonian systems close to integrable'', with A. Bounemoura, arXiv:1412.7455, preprint, 2014, 8pp, to appear in Proceedings of the American Mathematical Society, [PDF]
Spectral rigidity and Birkhoff conjectureo `` An integrable deformation of an ellipse of small eccentricity is an ellipse'', with A. Avila, J. De Simoi, arXiv:1412.2853, preprint, 22pp, 2014, [PDF]
Central Configurations and Smale's 6^{th} problemo `` Finiteness of central configurations of five bodies in the plane'', with A. Albouy, Annals of Mathematics 176, 535588, 2012, [PDF]
Growth of Sobolev norms for Hamiltonian PDEso `` Growth of Sobolev norms
in the cubic defocusing nonlinear Schodinger equation'',
with M. Guardia,
Examples of Arnold diffusiono `` Normally normally hyperbolic invariant manifolds near strong double resonance'', with K. Zhang, arXiv:1202.1032 [math.DS], 2012, 44pp, [PDF]
o ``An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension'', with M. Saprykina, Communications in Mathematical Physics, 315, 2012, 643697, 2012 [PDF]
o ``Almost dense orbit on energy surface'', with Ke Zhang and Yong Zheng, Proceedings of XVITH International Congress on Mathematical Physics. Held 38 August 2009 in Prague, Czech Republic. Edited by Pavel Exner (Doppler Institute, Prague, Czech Republic). Published by World Scientific Publishing Co, 314322, [PDF]
Arnold diffusion in a latticeo ``Arnold diffusion in a pendulum lattice'', with M. Levi and M. Saprykina, Volume 67, Issue 5, pages 748775, May 2014, Communications in Pure and Applied Mathematics, [PDF]
Oscillatory motions and Cantor sets of large Hausdorff dimensiono ``Conservative homoclinic bifurcations and some applications'', with A. Gorodetski, Steklov Institute Proceedings, Vol. 267 (2009), dedicated to the 70^{th} anniversary of Vladimir Arnold, [PDF] o ``Hausdorff dimension of oscillatory motions for restricted threebody problems'', with A. Gorodetski, preprint, 2013, 75pp, [PDF]
Instabilities for the threebody problemo ``Kikrwood gaps and diffusion along mean motion resonance
for the restricted planar three body problem'', with J. Fejoz, M.
Guardia, P. Roldan, arXiv:1109.2892 [math.DS] 2013, to appear in Journal of the European Mathematical Society, [PDF] o ``Destruction of invariant curves in the restricted
planar circular three body problem using action comparison'', with J. Galante, Duke Math J,
vol. 159, no. 2 (2011), 275327, [PDF] o `` The method of spreading cumulative twist and
application to the restricted planar circular three body problem'', with J. Galante, preprint, 2010, 48pp, [PDF] o ``Destruction of invariant curves in the restricted planar circular three body problem using ordering condition'', with J. Galante, preprint, 2010, 28pp, [PDF]
o ``Global instability in the elliptic restricted three body problem'', with A. Delshams, A. de la Rosa, T. Seara, arXiv:1501.01214, preprint, 2014, 41pp, [PDF]
Prevalenceo ``Prevalence, with B. Hunt , chapter
2, Handbook in dynamical systems, edited by H. Broer,
F. Takens, B. Hasselblatt,
Vol. 3, 2010, pg. 4387, [PDF]
List of my older papers and preprints ordered
by topics [PDF]
List of my older papers and preprints in
chronological order
[PDF] 

