I work in the field of Dynamical systems theory and its applications. This field deals with how systems evolve with time. It is well established by now that even very simple deterministic systems can have complicated, even chaotic, dynamics. Studying the characteristics of chaotic motions that arise in fluid mixing, particle dynamics and nonlinear optics problems leads to new insights on the physics and to new developments of the mathematical theory. Modeling the innate immune system of cancer patients and using dynamical systems tools to analyze the model lead to suggesting novel strategies of treatment for the patients.
- [with A.C. Poje] Universal properties of chaotic transport in the presence of diffusion. Phys. Fluids 11 (8) (1999) 2044-2057.
- [with A. Litvak-Hinenzon] On energy surfaces and the resonance web. SIAM J. Appl. Dyn. Syst. 3 (4) 525-573, 2004.
- [with E. Shlizermann] Three types of chaos in the forced nonlinear Schrodinger equation. Phys. Rev. Lett. 96, 024104, 2006.
- [with A. Rapoport and D. Turaev] Stability in high dimensional steep repelling potentials. Comm. Math. Phys. 279 (2008) 497-534.
- [with A. Rapoport] Chaotic scattering by steep potentials. Phys. Rev E. 77, 016207, 2008.
- [with E. Shochat] Novel strategies for G-CSF treatment of high-risk severe neutropenia suggested by mathematical modeling. Clinical Cancer Research, 2008, to appear.