Self Similarity, Critical Points, and Hill’s Spherical Vortex

SELF-SIMILARITY AND UNIVERSALITY IN CHUA'S CIRCUIT VIA THE APPROXIMATE CHUA'S 1-D MAP

Journal of Circuits System and Computers ◽

10.1142/s0218126693000265 ◽

1993 ◽

Vol 03 (02) ◽

pp. 431-440 ◽

Cited By ~ 1

Author(s):

A. P. KUZNETSOV ◽

S. P. KUZNETSOV ◽

I. R. SATAEV ◽

L. O. CHUA

Keyword(s):

Renormalization Group ◽

Critical Points ◽

Renormalization Group Equation ◽

Group Equation ◽

Chua’S Circuit ◽

Self Similarity ◽

One Dimensional ◽

Chua's Circuit ◽

Transition To Chaos ◽

Self Similar

In this paper we investigate the features of the transition to chaos in a one-dimensional Chua's map which describes approximately the Chua's circuit. These features arise from the nonunimodality of this map. We show that there exists a variety of types of critical points, which are characterized by a universal self-similar topography in a neighborhood of each critical point in the parameter plane. Such universalities are associated with various cycles of Feigenbaum's renormalization group equation.

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The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽

10.1017/s0094837300025707 ◽

1980 ◽

Vol 6 (02) ◽

pp. 146-160 ◽

Cited By ~ 29

Author(s):

William A. Oliver

Keyword(s):

Critical Points ◽

Scleractinian Corals ◽

Convincing Evidence ◽

Early Triassic ◽

Rugose Corals ◽

History Of ◽

The Subject ◽

Relationship Of ◽

The Relationship ◽

Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

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