Titlebook: Averaging Methods in Nonlinear Dynamical Systems; Jan A. Sanders,Ferdinand Verhulst,James Murdock Book 2007Latest edition Springer-Verlag

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https://doi.org/10.1007/978-3-642-94414-7solutions and estimate their error, but also to prove the existence of periodic orbits and determine their stability. With more recent developments in dynamical systems theory, it has become possible to study not only these local qualitative properties, but also global ones, such as the existence of

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https://doi.org/10.1007/978-3-642-48555-8tion is defined. In Section 3.2 this process was formalized using the Lie method. We are now going to develop a completely abstract theory of normal forms that generalizes the averaging approach. This will require of the reader a certain knowledge of algebraic concepts, which we will indicate on the

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https://doi.org/10.1007/978-3-642-48555-8ms, a basic approach is to locate and to characterize the classical ingredients of such systems. These ingredients are critical points (equilibrium solutions), periodic solutions, invariant manifolds (in particular quasiperiodic tori), homoclinics, heteroclinics, and in general stable and unstable m

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https://doi.org/10.1007/978-3-642-48555-8oday one can discern, rather artificially, three problem fields. The first one is the study of classical problems like perturbed Kepler motion, orbits in the threebody problem, the theory of asteroids and comets, etc. The second one is a small but relatively important field in which the astrophysici