By Arieh Iserles

ISBN-10: 0521818761

ISBN-13: 9780521818766

Acta Numerica anually surveys an important advancements in numerical arithmetic and clinical computing. the topics and authors of the important articles are selected by way of a wonderful foreign editorial board, with a view to file an important and well timed advancements in a way available to the broader group of execs with an curiosity in medical computing. Acta Numerica volumes are a useful instrument not just for researchers and execs wishing to advance their realizing of numerical innovations and algorithms and stick to new advancements. also they are used as complex instructing aids at faculties and universities (many of the unique articles are used because the best source for graduate courses).

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**Extra resources for Acta Numerica 2002: Volume 11**

**Example text**

In general, the appearance of a fractal geometry along both the stable and the unstable manifolds and the existence of a horseshoe type of structure are indications that a chaotic saddle exists in the phase space of interest. Note that if the manifolds of the hyperbolic orbit chosen do not intersect each other, the orbit does not belong to a chaotic saddle. In this case, it is necessary to choose a different periodic orbit to start with. 2 Ensemble Method The idea of this method, introduced by Kantz and Grassberger [380], is to follow an ensemble of trajectories and select the pieces that remain in the vicinity of the saddle.

8) is valid by the first time step. We see that ρc is thus the special initial distribution for which n∗ = 1. The c-measures of one-dimensional maps will be studied in detail in the next chapter. Here we briefly describe the construction of the c-measure for invertible two-dimensional maps. For such a system, the c-measure can be defined as follows [341]. Since trajectories escape the chaotic saddle along the unstable manifold, after n 1 iterations, the surviving trajectory points of number Nn in Γ will be in the vicinity of the unstable manifold.

In an experiment by In et al. [351], chaos in a magnetoelastic ribbon was successfully maintained at a parameter set where a fixed-point attractor exists; see Fig. 22. The quantity Xn plotted is proportional to the position of a point on the ribbon measured once every driving period of an applied external magnetic field. 10 Turbulence in Pipe Flows In a pipe flow, a steady laminar solution is linearly stable for all Reynolds numbers Re ≡ UD/ν , where U is the average velocity in a pipe of diameter D, and ν is the kinematic viscosity.

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