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Applications of Lie systems in quantum mechanics and control theory

José F. Cariñena, Arturo Ramos (2003)

Banach Center Publications

Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study...

Applications of symplectic homology I.

H. Hofer, K. Wysocki, A. Floer (1994)

Mathematische Zeitschrift

Applications of symplectic homology II: Stability of the action spectrum.

K. Wysocki, A. Floer, K. Cieliebak (1996)

Mathematische Zeitschrift

Approximation of invariant surfaces by periodic orbits in high-dimensional maps: Some rigorous results.

Tompaidis, Stathis (1996)

Experimental Mathematics

Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems

Marek Izydorek, Joanna Janczewska (2014)

Banach Center Publications

In this work we will consider a class of second order perturbed Hamiltonian systems of the form $q ̈ + V_{q} (t, q) = f (t)$ , where t ∈ ℝ, q ∈ ℝⁿ, with a superquadratic growth condition on a time periodic potential V: ℝ × ℝⁿ → ℝ and a small aperiodic forcing term f: ℝ → ℝⁿ. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system is obtained...