On self-similarity in homogeneous quadratic transformations

Yoshikawa, Takeshi; Da-tc, Tsutomu
May 2000
AIP Conference Proceedings;2000, Vol. 517 Issue 1, p574
Academic Journal
In this paper, we derive invariants for discriminating the existence of self-similar parts in the shape of a divergence-convergence boundary of two-dimensional real homogeneous quadratic transformations. A self-similar part in this context includes an infinite number of its own contracted images ranging closely. To explain the properties of this shape, we analyze the self-similarity in the portrait of the behavior of directions in the transformation process. For two-dimensional real homogeneous quadratic transformations, Da-te and Iri gave the invariant series in Ref. (4). We found an additional invariant to discriminate the existence of self-similar parts. © 2000 American Institute of Physics.


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