Abstract
This chapter gives a brief introduction to the geometric theory of autonomous Hamiltonian systems by studying some local questions about the nature of the solutions in a neighborhood of a point or a periodic solution. The dependences of periodic solutions on parameters are also presented in the case when no drastic changes occur, i.e., when there are no bifurcations. Bifurcations are addressed in detail in Chapter 11
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Meyer, K.R., Offin, D.C. (2017). Local Geometric Theory. In: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Applied Mathematical Sciences, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-53691-0_6
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DOI: https://doi.org/10.1007/978-3-319-53691-0_6
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