Professor Vassili Gelfreich
Vassili Gelfreich Professor of Mathematics Office: B2.07 |
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
Publications:
2018
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.)
2017
K. Shah, D. Turaev, V. Gelfreich, V. Rom-Kedar, Equilibration of energy in slow-fast systems, PNAS 2017 December, 114 (49) E10514-E10523 https://doi.org/10.1073/pnas.1706341114
V. Gelfreich, D. Turaev, "Arnold Diffusion in a priory chaotic symplectic maps", Commun. Math. Phys. (doi:10.1007/s00220-017-2867-0)
2015
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)
2014
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]
2013
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
2012
Gelfreich V., Rom-Kedar V., Turaev D., Fermi acceleration and adiabatic invariants for non-autonomous billiards, Chaos 22, 033116 (2012).
2010
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)
2009
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)
2008
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 2. 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