Gelfreich V., Brännström N. (2008)
Asymptotic series for the splitting of separatrices near a Hamiltonian bifurcation. arXiv:0806.2403v1 [math.DS] )

Recent Publications:

V. Gelfreich , C. Simo and A. Vieiro (2012),
Dynamics of 4D symplectic maps near a double resonance, Physica D (in print)
Gelfreich V., Rom-Kedar V., Turaev D. (2012),
Fermi acceleration and adiabatic invariants for non-autonomous billiards, Chaos 22, 033116 (2012).
Betz V., Gelfreich V. and Theil F.,
Oscillatory Sums, The Mathematical Intelligencer (2011)
Gelfreich V., Rom-Kedar V., Shah K., Turaev D. (2011)
Robust Exponential Acceleration in Time-Dependent Billiards, Phys. Rev. Lett. 106, 074101
Gaivao J.P. and Gelfreich V. (2011)
Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the Swift-Hohenberg equation as an example, Nonlinearity 24, no.3 (2011) pp. 677-698
Gelfreich V., Turaev D. (2010)
Universal dynamics in a neighborhood of a generic elliptic periodic point. Regular and Chaotic Dynamics vol. 15 no. 2-3 (2010) 159-164
Brännström N., De Simone E., Gelfreich V. (2010),
Geometric Shadowing in Slow-Fast Hamiltonian Systems, Nonlinearity 23 1169 (Preprint arxiv: 0905.3087)
Gelfreich V., Gelfreikh N. (2010)
Unique normal forms for area preserving maps near a fixed point with neutral multipliers, Regular and Chaotic Dynamics, vol. 15 no. 2-3 (2010) 300-318 (Preprint 2009)
Gelfreich V., Gelfreikh N. (2009)
Unique resonant normal forms for area-preserving maps at an elliptic fixed point. Nonlinearity 22 (2009), 783-810, (Preprint, September 2008; arXiv:0809.1614)
Gelfreich V., Naudot V. (2009)
Width of homoclinic zone for quadratic maps, Experimental Mathematics 18:4 (2009) 409-427 (Preprint: arXiv:0805.0324v1)
Gelfreich V., Turaev D.
Fermi acceleration in non-autonomous billiards, J. Phys. A: Math. Theor. 41 (2008) 212003 (6pp) (preprint)
Gelfreich V., Turaev D.
Unbounded energy growth in Hamiltonian systems with a slowly varying parameter. Comm. Math. Physics Vol. 283, Num. 3 (2008) 769-794. (Preprint on mp_arc no. 07-215)
Brännström N., Gelfreich V.
Drift of slow variables in slow-fast Hamiltonian systems. Physica D 237 (2008) 2913–2921 (Preprint 2007 arXiv:0710.1576v2 )
Butler L., Gelfreich V.
Positive-entropy geodesic flows on Nilmanifolds, Nonlinearity 21 (2008) 1423-1434 (preprint arXiv:0709.4646 )
Gelfreich V., Naudot V. (2008)
Analytic invariants associated with a parabolic fixed point in C2, Ergodic Theory and Dynamical Systems, vol. 28, iss. 06 (2008) 1815-1848
Gelfreich V., Simo C.
High-precision computations of divergent asymptotic series and homoclinic phenomena, Discrete and Continuous Dynamical Systems, Series B vol.10 (2008), no. 2/3, 511-536 Preprint

Other Publications:

Lerman L., Gelfreich V. (2005)
Fast-slow Hamiltonian dynamics near a ghost separatrix loop.
J. Math. Sci. (N. Y.) 126 (2005), no. 5, 1445-1466
Gelfreich, V.; Lerman, L. M. (2005)
Slow manifolds in a singularly perturbed Hamiltonian system. EQUADIFF 2003, 889--894, World Sci. Publ., Hackensack, NJ, 2005
Gelfreich V. (2004)
Hamiltonian bifurcations and local analytic classififcation, in Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Kluwer, 251--265
Gelfreich V.; Lerman L. (2003)
Long-periodic orbits and invariant tori in a singularly perturbed Hamiltonian system, 
Physica D Vol 176 Iss 3 - 4, pp 125-146 (Mathematical Physics Preprint Archive , no. 02-187), 23 p.   get a copy, pdf (836 K)
Gelfreich V. (2003)
Chaotic zone in the Bogdanov-Takens bifurcation for diffeomorphisms, in Analysis and Applications - ISAAC 2001, edited by H. Begehr, R. Gilbert, Man-Wah Wong, Kluwer, pp. 187--197  (Mathematical Physics Preprint Archive, no. 02-21), 12 p. revised version, ps (637 K)
Gelfreich V.; Lerman L. (2002)
Dynamical Properties of a Singularly Perturbed Hamiltonian System Near Its Slow Manifold
(Russian) Vol. 66, No. 3, 403--406 (Russian, ps, 173 K)
Gelfreich V. (2002)
Near strongly resonant periodic orbits in a Hamiltonian system. Proc. Nat. Acad. Sci. USA, vol. 99, no. 22, pp.13975-13979.   
(Mathematical Physics Preprint Archive , no. 00-402)
Gelfreich V., Lerman L. (2002)
Almost invariant elliptic manifolds in a singularly perturbed Hamiltonian system, Nonlinearity, vol. 15, pp.447--457.  
(Mathematical Physics Preprint Archive, no. 01-134, 12 p.) or the local copy ps.gz (80 K)
Gelfreich V. (2002)
Numerics and exponential smallness, in "Handbook of Dynamical Systems: vol. 2", B.Fiedler (ed.) Elsevier (2002) pp. 265--312.
Gelfreich V. (2001)
A century of separatrices splitting in Hamiltonian dynamical systems: perturbation theory, exponential smallness. XIII Int.Congr.on Math.Phys. (ICMP2000), Plenary lecture, London, July 17, 2000 A. Fokas, A. Grigoryan, T. Kibble, B. Zegarlinski (edts), International press, Boston (2001) pp. 73--86 ps.gz
Gelfreich V., Lazutkin V. (2001)
Splitting of Separatrices: perturbation theory and exponential smallness, Russian Math. Surveys Vol. 56, No. 3, pp. 499--558 (Uspekhi 2001, t. 56, vyp. 3., s. 79--142 (Russian)). ps.gz (1.5 MB, Russian) pdf file (Russian)
Gelfreich V., Sauzin D. (2001)
Borel summation and splitting of separatrices for the Henon map , Annales l'Institut Fourier, vol. 51, fasc. 2, p.513--567. % Preprint (ps.gz): Notes Sc. et Techn. du Bureau des Longitudes, S067, 48 p. (1999);
Gelfreich V. (2000)
Splitting of a small separatrix loop near the saddle-center bifurcation in area-preserving maps, Physica D 136, no.3--4, pp.266-279. % (Mathematical Physics Preprint Archive , no. 98-646)
Gelfreich V. (2000)
Exponentially small splitting of separatrices near bifurcations in area-preserving maps, Equadiff99. International Conference on Differential equations, Berlin 1999, vol.2, B. Fiedler et. al (edts); World Scientific, pp. 947-951
Gelfreich V. (2000)
Exponentially small splitting of separatrices for area-preserving maps. Chaos, Solitons and Fractals, vol. 11/1--3, pp. 241-243
Gelfreich V. (1999)
A proof of the exponentially small transversality of the separatrices for the standard map, Comm. Math. Phys. 201/1, pp. 155--216
Delshams A.; Gelfreich V.; Jorba A.; Seara T. M. (1999)
Splitting of separatrices for (fast) quasiperiodic forcing, in: C. Simo, editor, Hamiltonian Systems with Three or More Degrees of Freedom, NATO Sc. Ser.: C Math. Phys. Sci.; Kluwer Acad. Publ., vol. 533, pp. 367--371
Gelfreich V. (1998)
Analytical invariants of conformal transformations. A dynamical system approach. Regular and Chaotic Dynamics, vol. 3, no. 4, pp.42--50
Gelfreich V. (1998)
On Higher-order Melnikov Method for the Exponentially Small Splitting of Separatrices, Mathematical Physics Preprint Archive, no. 98-773
Delshams A., Gelfreich V. , Jorba A., Seara T. M. (1997)
Exponentially small splitting of separatrices under fast quasiperiodic forcing, Comm. Math. Phys. 189, pp. 35--71
Delshams A., Gelfreich V. , Jorba A., Seara T. M. (1997)
Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing, ERA AMS 3 (1) pp. 1--10
Fontich E., Gelfreich V. (1997)
On analytical properties of normal forms, Nonlinearity 10 (2) pp. 467--477
Gelfreich V. (1997)
Melnikov method and exponentially small splitting of separatrices , Physica D 101 (3-4) pp. 227--248
Gelfreich V. (1997)
Reference Systems for Splitting of separatrices, Nonlinearity 10 (1) pp. 175--193
Gelfreich V. (1996/2000)
Separatrix Splitting for a high-frequency perturbation of the pendulum , Russian Journal of Math. Physics (2000) vol. 7, no.1, pp.48--71 % Universitat de Barcelona, Mathematics preprint series no.195, January 1996, 29 p.
Gelfreich V. (1996)
Conjugation to a shift and splitting of separatrices, Applicationes Mathematicae 24, 2, pp. 127--140
Gelfreich V., Sharomov D.K. (1995)
Examples of Hamiltonian systems with transversal homoclinic orbits , Physics Letters A 197, pp. 139--146.
Gelfreich V., Lazutkin V.F., Svanidze N.V. (1994)
A refined formula for the separatrix splitting for the standard map. Physica D 71, no. 2, pp. 82--101.
Gelfreich V. (1994)
Separatrices splitting for the rapidly forced pendulum, "Seminar on Dynamical Systems". Euler International Math. Institute, St.Petersburg 1991", Birkhauser, pp. 47--67.
Gelfreich V. (1992)
Separatrices splitting for some polynomial Hamiltonian systems close to the integrable ones, PhD, St.Petersburg University
Gelfreich V., Lazutkin V.F., Simo C., Tabanov M.B. (1992)
Fern like structures in the wild set of the standard and semistandard maps in $C^2$, International Journal of Bifurcation and Chaos 2, no. 2, pp. 353--373.
Gelfreich V.G., Lazutkin V.F., Tabanov M.B. (1991)
Exponentially small splittings in Hamiltonian systems, Chaos 1, no. 2, pp. 137--142.
Gelfreich V.G. (1991)
Separatrices splitting for the polynomial area-preserving maps , in: Topics in Mathematical Physics 13, M. Sh. Birman (ed.) pp. 108--117 (Russian).
Gelfreich V.G. (1990)
Computation of analytical invariants of conform maps near degenerate fixed point, in: Mathematical Methods in Engineering, S.A. Ponyrko (ed.), SIAP, pp. 77--79 (Russian).
Gelfreich V.G. (1988)
Separatrices splitting for a standard family of area-preserving diffeomorphisms, VINITI, no. 3234-B88, 22 p. (Russian)