Examples of renormalization

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We now want to determine the tangent renormalization operator.
Thus, in particular, the appearance of the continued fractions is no accident; it comes from the renormalization of circle rotations.
Some of our results are sufficiently general to be used, for example, in other problems involving renormalization.
We are now in a position to deal with the hyperbolicity of the renormalization.
Let us also briefly comment on the interplay between renormalization and flowequivalence.
For the two kinds of renormalization, the maps we are interested in are infinitely renormalizable.
Long-term renormalization visual system than the site of discrimination (unless the two processes are parallel).
The renormalization method of quasilinear equations to treat the diffusion of magnetic force lines is considered.
This approach aims to classify vector fields according to the arithmetic properties of their flows, with the equivalence classes being stable manifolds under renormalization.
The necessary counterparts of corresponding renormalization in the diagrams of 'mass operator' are embedded in the same diagrams 5-8.
The convergence of renormalization is implied by the combinatorial rigidity of the corresponding limiting bi-infinite towers.
That is, the maps in the limiting towers are related by either classical or parabolic renormalization.
However, the isolated points will always be preimages of periodic points which form the boundary of domains of renormalization.
Despite the lack of differentiability, the spectral properties of the tangent renormalization will reflect the action of the renormalization itself.
Furthermore, we show that the principle of topological renormalization is false for attracting exponential maps.
The classification of renormalization limits for bounded combinatorics holds for a more general class of maps.
We can now state the combinatorial classification of all limits of renormalization of an infinitely renormalizable real quadratic with essentially bounded combinatorics.
It follows that renormalization can reduce the boundary-layer equations to the case of p = 0 with a separation angle identical with that of non-rotating flows.
Our first result produces the analog of the renormalization fixed point in the essentially period tripling situation.

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