dynamical systems; integrability of hamiltonian systems; invariant manifolds; symbolic dynamics; singularities of twist maps; normal forms.
Main publications:
A. V. Ivanov. Study of the double mathematical pendulum - I. Numerical investigation of homoclinic transversal intersections // Regul. Chaotic Dyn., 4(1), 104–116, 1999.
A. V. Ivanov. Study of the double mathematical pendulum - II. Investigation of exponentially small transversal intersections // J. Phys. A: Math. Gen., 34 (2001), 11011–11031.
A. V. Ivanov. Study of the double mathematical pendulum - III. Menikov's method applied to the system in the limit of small ratio of pendulums masses // Regul. Chaotic Dyn., 5(3), 329–344, 2000.
Natalia G. Gelfreikh, Alexey V. Ivanov, “Slow-Fast Systems with an Equilibrium Near the Folded Slow Manifold”, Regul. Chaotic Dyn., 29:2 (2024), 376–403
2023
2.
Alexey V. Ivanov, “On $SL(2,\mathbb{R})$-Cocycles over Irrational Rotations with Secondary Collisions”, Regul. Chaotic Dyn., 28:2 (2023), 207–226
Alexey V. Ivanov, “On Transversal Connecting Orbits of Lagrangian Systems in a Nonstationary Force Field: the Newton – Kantorovich Approach”, Regul. Chaotic Dyn., 24:4 (2019), 392–417
2017
5.
Alexey V. Ivanov, “Connecting Orbits near the Adiabatic Limit of Lagrangian Systems with Turning Points”, Regul. Chaotic Dyn., 22:5 (2017), 479–501
A. V. Ivanov, “Study of the Double Mathematical Pendulum — IV. Quantitative Bounds on Values of the System Parameters when the Homoclinic Transversal Intersections Exist”, Regul. Chaotic Dyn., 6:1 (2001), 53–94
A. V. Ivanov, “Study of the Double Mathematical Pendulum — III. Melnikov's Method Applied to the System In the Limit of Small Ratio of Pendulums Masses”, Regul. Chaotic Dyn., 5:3 (2000), 329–343
A. V. Ivanov, “Study of the double mathematical pendulum — I. Numerical investigation of homoclinic transversal intersections”, Regul. Chaotic Dyn., 4:1 (1999), 104–116
Contact us: