scholarly journals Rigidity of critical circle mappings I

1999 ◽  
Vol 1 (4) ◽  
pp. 339-392 ◽  
Author(s):  
Edson de Faria ◽  
Welington de Melo
Keyword(s):  
Critical Circle ◽  
Circle Mappings

scholarly journals Rigidity of critical circle mappings II

1999 ◽  
Vol 13 (2) ◽  
pp. 343-370 ◽  
Author(s):  
Edson de Faria ◽  
Welington de Melo
Keyword(s):  
Critical Circle ◽  
Circle Mappings

Asymptotic rigidity of scaling ratios for critical circle mappings

1999 ◽  
Vol 19 (4) ◽  
pp. 995-1035 ◽  
Author(s):  
EDSON DE FARIA
Keyword(s):  
Critical Point ◽  
Surgical Techniques ◽  
Careful Analysis ◽  
The Family ◽  
Critical Circle ◽  
Renormalization Operator ◽  
Irrational Rotation Number ◽  
Circle Mappings ◽  
Commuting Pairs ◽  
Unimodal Mappings

Let $f$ be a smooth homeomorphism of the circle having one cubic-exponent critical point and irrational rotation number of bounded combinatorial type. Using certain pull-back and quasiconformal surgical techniques, we prove that the scaling ratios of $f$ about the critical point are asymptotically independent of $f$. This settles in particular the golden mean universality conjecture. We introduce the notion of a holomorphic commuting pair, a complex dynamical system that, in the analytic case, represents an extension of $f$ to the complex plane and behaves somewhat as a quadratic-like mapping. We define a suitable renormalization operator that acts on such objects. Through careful analysis of the family of entire mappings given by $z\mapsto z+\theta -(1/2\pi)\sin{2\pi z}$, $\theta$ real, we construct examples of holomorphic commuting pairs, from which certain necessary limit set pre-rigidity results are extracted. The rigidity problem for $f$ is thereby reduced to one of renormalization convergence. We handle this last problem by means of Teichmüller extremal methods made available through the recent work of Sullivan on Riemann surface laminations and renormalization of unimodal mappings.

The Critical Circle

1982 ◽  
Author(s):  
David Couzens Hoy
Keyword(s):  
Critical Circle

scholarly journals The Rigidity Problem for Analytic Critical Circle Maps

2006 ◽  
Vol 6 (2) ◽  
pp. 317-351 ◽  
Author(s):  
D. Khmelev ◽  
M. Yampolsky
Keyword(s):  
Circle Maps ◽  
Critical Circle

“A Fabric of Illusion”

2017 ◽  
Author(s):  
Brian Cremins
Keyword(s):  
Comic Book ◽  
Critical Circle ◽  
Comic Art

C. C. Beck was one of the most influential artists working in comics in the U. S. in the 1940s and 1950s. As the co-creator of Captain Marvel, he and his assistants worked on one of the best-selling comic book characters of the era. Later in his career, he also developed a reputation as a comics critic. In addition to his columns for The Comics Journal, he established the Critical Circle in the late 1980s, a group of friends, fellow artists, and fans with whom he shared his unpublished essays on the form. Like Will Eisner, Beck was significant as a cartoonist and as a theorist of comic art. This chapter explores how he applied those theories to his work, which is known for its narrative economy and simplicity.

Pseudo-Static Analysis of Slope Considering Circular Rupture Surface

2014 ◽  
Vol 5 (2) ◽  
pp. 37-43 ◽  
Author(s):  
Sima Ghosh
Keyword(s):  
Factor Of Safety ◽  
Limit Equilibrium ◽  
Slope Angle ◽  
Failure Surface ◽  
Friction Angle ◽  
Equilibrium Analysis ◽  
Seismic Slope Stability ◽  
Slide Mass ◽  
Critical Circle ◽  
Seismic Forces

In this present paper, a circular failure surface passing through the toe is assumed for a homogeneous soil, and the Fellenius line is used to locate the centre of the most critical circle. Using limit equilibrium analysis under the influence of static forces such as weight of potential slide mass and surcharge along with the pseudo-static seismic forces are considered to obtain the factor of safety of the slopes. Factor of safety is found through the application of force equilibrium. The effects of variation of different parameters like slope angle (i), soil friction angle (F) and seismic acceleration coefficients both in the horizontal and vertical directions (kh and kv respectively) on the factor of safety are presented. Finally, the present results are compared to the existing solutions available in literature and found to give minimum values of factor of safety using the present approach for seismic slope stability analysis.

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