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By Korsch H., Jodl H., Hartmann T.
This new version strives another time to supply readers with a operating wisdom of chaos concept and dynamical platforms. It does so via parallel introductory causes within the ebook and interplay with carefully-selected courses provided at the accompanying disk. The courses permit readers, specially advanced-undergraduate scholars in physics, engineering, and math, to take on proper actual platforms speedy on their computers, with no distraction from algorithmic info. For the 3rd variation of Chaos: A software assortment for the computer, all the earlier twelve courses is polished and rewritten in C++ (both home windows and Linux types are included). a brand new application treats kicked structures, a big type of two-dimensional problems.
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Extra resources for Chaos: A Program Collection for the PC
Sample text
Almost all trajectories get arbitrarily close to any point on the energy surface. 3 Dissipative Dynamical Systems An important feature of the Hamiltonian systems discussed in the preceding section is the conservation of the volume element in phase space. For a dissipative system, this volume element contracts and the trajectory approaches a (lower-dimensional) subset of the phase space, an ‘attractor’ . , their bifurcation properties. 27) where x = (x1 , . . , xN ) is a vector in N -dimensional phase space, and v = (v1 , .
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S. Smale, Diffeomorphisms with many periodic points, in S. S. Cairns, editor, Differential and Combinatorial Topology. Princeton University Press, Princeton, 1963 14. D. Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys. 20 (1971) 167, reprinted in: Hao Bai-Lin, Chaos, World Scientific, Singapore, 1984 15. S. E. Newhouse, D. Ruelle, and F. Takens, Occurrence of strange axiom A attractors near quasiperiodic flows on T m , m ≥ 3, Commun. Math. Phys. 64 (1978) 35 16. P. Manneville and Y.