Directions of research
- theory of dynamical systems, in particular:
- non-integrability problems for systems depending on many parameters;
- chaotic dynamics;
- splitting of invariant manifolds;
- asymptotic and variational methods for constructing special classes of solutions of Hamiltonian systems.
Basic Research papers
- A.V. Ivanov, Study of the double mathematical pendulum — II. Investigation of exponentially small homoclinic intersections, Journal Physica A: General and Mathematical, 2001, v. 34,
- H.R. Dullin, A.V. Ivanov, Vanishing Twist in the Hamiltonian Hopf bifurcation, Physica D, 2005, v. 201, pp. 27-44.
- H.R. Dullin, A.V. Ivanov, J.D.Meiss, Normal forms for symplectic maps with singularties, Physica D, 2006, v. 213, pp. 175-190
- 3rd year course in methods of mathematical physics (practice);
- Special course for postgraduate students: «Introduction to symplectic geometry and Hamiltonian systems».