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Hamiltonian Systems and conservation of energy (Master thesis)

Ψαροπουλος, Ιωάννης/ Psaropoulos, Ioannis/ Εφαρμοσμένα Μαθηματικά/ Applied Mathematics

A class of dynamical systems are Hamiltonian systems, as well as derived systems or potential systems. These are related to the dynamics of motion of classical systems derived from Newton's second law. In Hamiltonian systems, features such as conservation laws, complex structure, Poisson brackets, etc. appear with which we can study these systems more analytically. The study of linear systems in two dimensions is extended to nonlinear systems. We focus on finding and classifying critical points and define hyperbolic and non hyperbolic critical points. A characteristic of autonomous dynamical systems is the appearance of a specific type of orbit, which has the form of a closed curve, called a limit cycle and represents a periodic solution of the system. Limit cycles can appear in systems of any order and are a typical form of oscillation.