My webpage has moved to
http://www.terpconnect.umd.edu/~vkaloshi/
Vadim Kaloshin 


266 Sloan 


Teaching Spring 2004: Mathematical Chaos (Undegraduate) 

Research My research interests include smooth and random dynamical systems and Hamiltonian systems, in particular, AubryMather theory and Arnold diffusion. Research papers sorted by topics: I. Smooth dynamical systems: Growth of the number of
periodic points and Newhouse phenomenon 1. ``An extension of ArtinMazur theorem'', Annals of Mathematics, Vol 150, No. 2, (1999), 429441, online ; 2. ``Generic diffeomorphisms with superexponential
growth of number of periodic points'', Comm. in
Math. Physics,Vol
211, (2000), 1, 253271, online; 3. ``Growth of the number of
periodic points'', in Normal forms, Bifurcations and Finiteness Problems in
Differential Equations (eds. Y. Ilyashenko and C.
Rousseau), Kluwer 2004, 355385, online;
4. (with B.Hunt)
''A stretched exponential bound on the rate of growth of the number of
periodic points for prevalent diffeomorphisms'', I
& II. Electron. Res. Announc. Amer. Math. Soc.
7 (2001), 1727 online; & 2836,
online; 5. (with B.Hunt)
``A stretched exponential bound on the rate of growth of the number of
periodic points for prevalent diffeomorphisms'',
part I, to appear in Annals of Mathematics, 94pp, online; 6. ``A stretched exponential
bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms'', part II, preprint, (2002), 85pp, online; 7. (with A. Gorodetski) ``How often surface diffeomorphisms
have infinitely many sinks and hyperbolicity of
periodic points near a homoclinic tangency'', to
appear in Advances in Mathematics, 99p, online;
8. (with O. Kozlovsky) ``A C^r unimodal map with an arbitrary fast growth of the number
of periodic points'', preprint, (2002), 5pp, online;
9. (with
M. Saprykina) ``Generic 3dimensional
volumepreserving diffeomorphisms with superexponential growth of number of periodic orbits'',
Discrete Contin. Dyn.
Syst. 15 (2006), no. 2, 611640, online; 10. (with A. Gorodetski, B.Hunt) ``Newton
interpolation polynomials, discretization method, and certain prevalent
properties in dynamical systems'', notes for the 2006 ICM talk, 29pp, online; II. Instabilities in Hamiltonian systems and Arnold diffusion 11. ``Geometric proofs of
Mather's accelerating and connecting theorems'', Topics in Dynamics and Ergodic Theory (eds. S. Bezuglyi
and S. Kolyada), London Mathematical Society,
Lecture Notes Series, Cambridge University Press, 2003, 81106, online; 12. ``Mather theory, weak KAM,
and viscosity solutions of HamiltonJacobi PDE's'', EQUADIFF 2003,
3948, World Sci. Publ., Hackensack, NJ, 2005, online; 13. (with J. Bourgain) ``Diffusion for Hamiltonian perturbations of integrable systems in high dimensions'', J. of Func Analysis, 229, (2005), no 1, 161, online; 14. (with
J. Mather and E. Valdinoci) ``Instability of totally
elliptic points of symplectic maps in dimension
4'', Instability of resonant totally elliptic points of symplectic
maps in dimension 4. Analyse complexe,
systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes. II. Astérisque No.
297 (2004), 79116, online; 15. (with T. Nguyen) ``Remote
Periodic and Quasiperiodic Motions in the Planar
Circular Restricted 3Body Problem of KAM and AubryMather
Type'', preprint, 35pp, online; III. The Hilbert 16th problem and bifurcation theory 16. ``HilbertArnold Problem
and an estimate for cyclicity of polycycles on the plane and in the space'', Func Anal and its Appl, 35, no.
2, (2001), 146147, online; 17. (with Yu.S.Ilyashenko)
``Bifurcations of planar and spatial polycycles:
Arnold's program and its development'', Fields Institute Communications, 24,
(1999), 241271, online; 18. ``The Existential Hilbert
Problem and an estimate on cyclicity of elementary polycycles'', Inventiones Mathematica, 151 (2003), no. 3, 451512, online; 19. ``Around HilbertArnold
Problem'', in ``On finiteness in differential
equations and Diophantine geometry'', 111162, CRM Monogr.
Ser., 24, Amer. Math. Soc., Providence, RI, 2005, online; IV. Random flows and random walks along orbits of dynamical systems 20. (with D. Dolgopyat and L. Koralov) ``Hausdorff Dimension of Linear Escape points for periodic
Stochastic Dispersions'', J. Stat. Physics, Vol
108, (2002), 943971, online; 21. (with D. Dolgopyat and L. Koralov)
``Sample Path Properties of Stochastic Flows'', Annals of Probability, Vol.
32, no. 1A, (2004), 127, online; 22. (with D. Dolgopyat and L. Koralov) ``A
Limit Shape Theorem for Stochastic Dispersions'', Comm. in Pure and Appl.
Math., vol. 57, no. 9, (2004), 11271158, online;
23. (with D. Dolgopyat and L. Koralov)
``Long time behaviour of periodic stochastic disperions'', to appear in Proceedings of ICMP 2002, 8pp,
online; 24. (with Ya.G.Sinai)
``Nonsymmetric random walks along orbits of ergodic automorphisms'', Amer.
Math. Soc. Transl.(2), 198, (2000), 109115, online;
25. (with Ya.G.Sinai)
``Simple random walks along orbits of Anosov diffeomorphisms'', Proc. of Steklov
Math. Inst., 228, (2000), 224233, online; V. Properties of Fractal Sets under Projections 26. (with B. Hunt) ``How
projections affect the dimension spectrum of fractal measures'', Nonlinearity, 10, (1997), no. 5,
10311046, online; 27. (with B. Hunt) ``Regularity
of of embeddings of
infinitedimensional fractal sets into finitedimensional spaces'', Nonlinearity,Vol 12, (1999), no. 5, 12631275 online; 28. (with B.Hunt
and W.Ott) ``The effect of projections on fractal
sets and measures in Banach spaces'', to appear in Ergodic Theory and Dynamical Systems, (2003), 23pp, online; VI. Notion of Prevalence or Probability one in nonlinear infinitedimensional spaces 29. ``Some prevalent properties
of smooth dynamical systems'', Proceedings of the Steklov
Institute of Mathematics, 213, (1997), 123151; 30. ``Prevalence in spaces of
smooth mappings and a prevalent KupkaSmale
theorem'' (in Russian), Dokl. Akad.
Nauk, 355, (1997), no. 3, 306307; 31. ``Prevalence in spaces of
finitely smooth mappings'', Functional Analysis and its Application, 31,
(1997), no. 2, 9599; VII. Diophantine properties of SO(3). 32. (with I.Rodnianski)
``Diophantine Properties of Elements of SO(3)'', Geom
and Func Anal, 11, (2001), 953970, online; VIII. Whitney stratification 33. ``A Geometric Proof of Existence
of Whitney Stratifications'', Mosc. Math. J. 5 (2005),
no.
1, 125133, online; 


