RATIU, TUDOR S. / Mathematics / Researchers

International Center for Scientific Research

Researchers

Mathematics / RATIU, TUDOR S.

tudor.ratiuepfl.ch

Position

Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.

He held visiting positions at prestigious research centers such as Max Planck Institute for Mathematics (Germany), Mathematical Sciences Institute at Cornell University, Erwin Schrödinger Institute for Mathematical Physics (Austria), Institute des Hautes Études Scientifiques (France), Isaac Newton Institute for Mathematical Sciences in Cambridge (England).

Research interests

Tudor Ratiu has worked in integrable systems, sympletic geometry, Hamiltonian dynamics and the bifurcation theory of conservative systems in the presence of symmetry, especially their link to singular reduction and the properties of the momentum map.

Prizes and awards

His contribution to mathematics was recognized by numerous awards and prizes. Among other honors, he was an A. P. Sloan Foundation Fellow in 1984-1987, a Humbold Prize winner in 1997, and won a Ferran Sunyer and Balaguer Prize for the year 2000.

Publications

Chossat, P., Lewis, D., Ortega, J.-P., and Ratiu, T.S. [1999] Bifurcation of relative equilibria in mechanical systems with symmetry.

Chossat, P., Ortega, J.-P., and Ratiu, T.S. [1999] Hamiltonian Hopf bifurcation with symmetry.

Ortega, J.-P., and Ratiu, T.S. [1999] Lecture notes on Hamiltonian singular reduction.

Ortega, J.-P. and Ratiu, T.S. [1999] Non-linear stability of singular relative periodic orbits in Hamiltonian systems with symmetry. J. Geom. Phys.

Ortega, J.-P. and Ratiu, T.S. [1999] A Dirichlet criterion for the stability of periodic and relative periodic orbits in Hamiltonian systems. J. Geom. Phys.

Ortega, J.-P. and Ratiu, T.S. [1999] Stability of Hamiltonian relative equilibria. Nonlinearity , 12(3):693-720.

Castrillón-Lopez, M., T.S. Ratiu, and S. Shkoller [1998] Reduction in principal fiber bundles: covariant Euler-Poincaré equations, Proc. Amer. Math. Soc.

Bloch, A.M., P. Crouch, J.E. Marsden, and T.S. Ratiu [1998] Discrete rigid body dynamics and optimal control, Proceedings of the 37th IEEE Conference on Decision and Control.

Marsden,. J.E., G. Misiolek, M. Perlmutter, and T.S. Ratiu [1998] Symplectic reduction for semidirect products and central extensions, Diff. Geom. and its Appl., 9, 173-212.

Holm, D.D., J.E. Marsden, and T.S. Ratiu [1998] Euler-Poincaré equations in geophysical fluid dynamics, Proceedings of the Isaac Newton Institute.

Ortega, J.-P. and Ratiu, T.S. [1998] Singular reduction of Poisson manifolds. Lett. Math. Phys., 46:359-372.

Cendra, H., D.D. Holm, J.E. Marsden, and T.S. Ratiu [1998] Lagrangian reduction, the Euler-Poincaré equations, and semidirect products, Amer. Math Soc. Transl., 186, 1-25.

Fassò, F. and T.S. Ratiu [1998] Compatibility of symplectic structures adapted to noncommutatively integrable systems, Journ. Geom. and Physics, 27, 199-220.

Holm, D.D., J.E. Marsden, and T.S. Ratiu [1998] The Euler-Poincaré equations and semidirect products with applications to continuum theories, Advances in Math., 137, 1-81. {pdf}.

Michor, P. and T.S. Ratiu [1998] On the geometry of the Bott-Virasoro group, Journal of Lie Theory, 8. 293-309. {pdf}

Holm, D. D., J. E. Marsden and T. S. Ratiu [1998] Euler-Poincaré models of ideal fluids with nonlinear dispersion, Phys. Rev. Lett., 349, 4173-4177. {pdf}.

Derks, G. and T.S. Ratiu [1998] Attracting curves in Navier-Stokes and reduced magnetohydrodynamics, The Royal Society. Proceedings: Math., Phys. and Eng. Sci., Series A, 454, 1407-1444. {pdf}.

Ortega, J.-P. and T.S. Ratiu [1997] Persistence and differentiability of critical relative elements in Hamiltonian systems with symmetry, C.R. Acad. Sci. Paris 325, Série I, 1107-1111.

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