Skip to main content Skip to navigation

Professor Vassili Gelfreich

  Prof Vassili Gelfreich

Vassili Gelfreich

Professor of Mathematics

Office: B2.07
Phone: +44 (0)24 7652 8331
Email: V dot Gelfreich at warwick dot ac dot uk

Teaching Responsibilities 2023/24:

Term 2: MA143 Calculus 2

Term 2: MA482 Stochastic Analysis

A portrait of Arnold diffusion (med res version but still a large file): This is an illustration of dynamics near a double resonance in a 4d symplectic map

Research Interests:

Dynamical Systems, conservative dynamics, bifurcation theory



V. Gelfreich, A. Vieiro, Interpolating vector fields for near identity maps and averaging, Nonlinearity, Volume 31, Number 9, 4263 (preprint arXiv:1711.01983, 28 p.)


K. Shah, D. Turaev, V. Gelfreich, V. Rom-Kedar, Equilibration of energy in slow-fast systems, PNAS 2017 December, 114 (49) E10514-E10523

V. Gelfreich, D. Turaev, "Arnold Diffusion in a priory chaotic symplectic maps", Commun. Math. Phys. (doi:10.1007/s00220-017-2867-0)


K. Shah, V. Gelfreich, V. Rom-Kedar, D. Turaev, Leaky Fermi accelerators, Phys. Rev. E 91, 062920. (doi: 10.1103/PhysRevE.91.062920) (preprint arXiv:1504.00897)


Gelfreich V., Lerman L., Separatrix splitting at a Hamiltonian 02iω bifurcation, Regular and Chaotic Dynamics (2014) Vol. 19, Issue 6, pp 635-655 (preprint arXiv:1409.3042)

Gelfreich V., Rom-Kedar V., Turaev D., Oscillating mushrooms: adiabatic theory for a non-ergodic system. J. Phys. A: Math. Theor. 47 395101

Gelfreich V., Gelfreikh N., Unique normal forms near a degenerate elliptic fixed point in two-parametric families of area-preserving maps. Nonlinearity 27 (2014) 1645-1667

Gelfreich V., Turaev D., Arnold Diffusion in a priory chaotic Hamiltonian systems, arXiv:1406.2945 [math.DS]


V. Gelfreich , C. Simó and A. Vieiro, Dynamics of 4D symplectic maps near a double resonance, Physica D vol.243 issue 1 (2013) pp. 92-110


Gelfreich V., Rom-Kedar V., Turaev D., Fermi acceleration and adiabatic invariants for non-autonomous billiards, Chaos 22, 033116 (2012).


Volker Betz, Vassili Gelfreich and Florian Theil, Oscillatory Sums, The Mathematical Intelligencer (2011)

Gelfreich V., Rom-Kedar V., Shah K., Turaev D. Robust Exponential Acceleration in Time-Dependent Billiards, Phys. Rev. Lett. 106 (2011), 074101

Gaivao J.P., 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 (preprint arXiv:1004.2054v1)


Brännström N., De Simone E., Gelfreich V., Geometric Shadowing in Slow-Fast Hamiltonian Systems (2010) Nonlinearity 23 1169 (Preprint: arxiv: 0905.3087)

Gelfreich V., Turaev D. Universal dynamics in a neighborhood of a generic elliptic periodic point. Regular and Chaotic Dynamics vol. 15 no. 2-3 (2010) 159-164 

Gelfreich V., Gelfreikh N. Unique normal forms for area preserving maps near a fixed point with neutral multipliers. Regular and Chaotic Dynamics, 2010, Vol. 15, No. 2–3, pp. 300–318 (Preprint)


Gelfreich V., Naudot V., Width of Homolinic Zone in the Parameter Space for Quadratic Maps, Experimental Mathematics 18:4 (2009) 409-427

Gelfreich V., Gelfreikh N., Unique resonant normal forms for area-preserving maps at an elliptic fixed point. Nonlinearity 22 (2009), 783-810 (Preprint)


Gelfreich V., Turaev D. Fermi acceleration in non-autonomous billiards, J.Phys.A: Math.Theor. 41 (2008) 21200, (preprint)

Brännström N., Gelfreich V. Drift of slow variables in slow-fast Hamiltonian systems, Physica D 237 (2008) 2913–2921

Gelfreich V., Turaev D. Unbounded Energy Growth in Hamiltonian Systems with a Slowly Varying Parameter, Comm. Math. Phys. vol. 283, no. 3 (2008) 769-794

Gelfreich V., Simó C., High-precision computations of divergent asymptotic series and homoclinic phenomena, DCDS-B, vol. 10 (2008), no. 2/3, 511-536

Gelfreich V., Naudot V., Analytic invariants associated with a parabolic fixed point in xs21022.  Ergodic Theory and Dynamical Systems vol. 28, issue 06 (2008) pp 1815-1848

Butler L., Gelfreich V., Positive-entropy geodesic flows on Nilmanifolds, Nonlinearity 21 (2008) 1423-1434

Other publications

Gelfreich V, Lazutkin V. Splitting of Separatrices: perturbation theory and exponential smallness. RUSSIAN MATHEMATICAL SURVEYS, 56, (2001), 499-558

Gelfreich V, Sauzin D. Borel summation and splitting of separatrices for the Henon map. ANNALES DE L INSTITUT FOURIER, 51, (2001), 513-567

Gelfreich V. Near strongly resonant periodic orbits in a Hamiltonian system. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES (USA),99,(2002),13975-13979


For more information and further publications see Vassili Gelfreich's homepage or his Expertise Profile