By Hans Jürgen Korsch, Hans-Jörg Jodl, Timo Hartmann
This re-creation strives another time to supply readers with a operating wisdom of chaos concept and dynamical platforms via parallel introductory motives within the e-book and interplay with carefully-selected courses provided at the accompanying diskette. The courses let readers, in particular advanced-undergraduate scholars in physics, engineering, and math, to take on proper actual structures fast on their computers, with out distraction from algorithmic info. For the 3rd version of Chaos: A application assortment for the computer, all the past twelve courses is polished and rewritten in C++ (both home windows and Linux models are included). a brand new application treats kicked platforms, an enormous category of two-dimensional difficulties, that's brought in bankruptcy thirteen. each one bankruptcy follows the constitution: theoretical heritage; numerical thoughts; interplay with this system; desktop experiments; actual experiments and empirical facts; reference. Interacting with the various numerical experiments have confirmed to aid readers to familiarize yourself with this attention-grabbing subject or even to benefit from the adventure.
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Additional info for Chaos: A Program Collection for the PC (3 rd. edition)
6 for more details). 4 Special Topics In order to assist the reader in a somewhat deeper analysis of the computer experiments, we present in this section some more specialized topics in nonlinear dynamics, which will be useful in many of the systems studied in the following computer experiments. The material is, however, slightly more technical and the connection and relevance to chaotic dynamics is not directly obvious. This section can be omitted at a ﬁrst reading. 1 The Poincar´ e-Birkhoﬀ Theorem According to the KAM theorem for Hamiltonian systems with two degrees of freedom (see Sect.
Here, we only note that a torus ﬁlled with periodic orbits with frequency ratio ω1 /ω2 = r/s quite typically decays. A number of ν s stable and ν s ( ν ∈ IN ) unstable periodic orbits are, however, still existent, where the integer ν is often equal to one (a periodic trajectory is called ‘stable’ if nearby trajectories remain close to it for all times). In a Poincar´e section, these s-periodic trajectories which persist in the perturbed system appear as stable or unstable ﬁxed points of the iterated Poincar´e map T s .
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