Interpretation:
To show that the map
To show that for small and positive r, it typically takes many iterations to pass through the bottleneck.
To find out how N(r) scales as
By expanding
To show that the equation in (d) has the solution
Concept Introduction:
Renormalization is based on the self-similarity of the Figtree- the twigs look like the earlier branches, except they are scaled down in both x and r directions. The Figtree structure shows an endless repetition of the same dynamical processes – a
Self-similarity is mathematically expressed as comparing
The function
The functional equation for
Here,
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Nonlinear Dynamics and Chaos
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage