Let f be a polynomial of degree d ≥ 2 in the complex plane and consider the following statements: (A d) " If f has a fixed Siegel disk ∆ of bounded type rotation number, then ∂∆ is a quasicircle passing through some critical point of f. " (B d) " If f has a fixed Siegel disk ∆ such that ∂∆ is a quasicircle passing through some critical point of f , then the rotation number of ∆ is bounded type....

We show that every complete metric space is homeomorphic to the locus of zeros of an entire analytic map from a complex Hilbert space to a complex Banach space. As a corollary, every separable complete metric space is homeomorphic to the locus of zeros of an entire analytic map between two complex Hilbert spaces. §1. Douady had observed [8] that every compact metric space is homeomorphic to the...

670 NOTICES OF THE AMS VOLUME 42, NUMBER 6 T he English word “prove”—as its Old French and Latin ancestors—has two basic meanings: to try or test, and to establish beyond doubt. The first meaning is largely archaic, though it survives in technical expressions (printer’s proofs) and adages (the exception proves the rule, the proof of the pudding). That these two meanings could have coexisted for...

That was not the topic of the talk (in fact, HD(∂M) = 2 had been proven 15 years earlier), so it was telling that they even knew what the notions were in the statement. To me, this conversation is symbolic of how much the language of complex dynamics has permeated mathematical culture since the early 1980s, when it was preposterous to think of doing serious research on the properties of quadrat...

Bibliography 207 Index 213 iii iv Chapter 1 Introduction 1.1 Complex dynamics This work presents a study of renormalization of quadratic polyno-mials and a rapid introduction to techniques in complex dynamics. Around 1920 Fatou and Julia initiated the theory of iterated rational maps f : C → C on the Riemann sphere. More recently methods of geometric function theory, quasiconformal mappings and...

The peptide toxin GsAF II (Kappa-theraphotoxin-Gr2c) is a 31-amino acid peptide, recently isolated from the venom of the tarantula spider Grammostola rosea. The peptide toxin ProTX II (β/ω-theraphotoxin-Tp2a), is a 30-amino acid peptide toxin recently isolated from the venom of the tarantula spider Thrixopelma pruriens. The GsAF II and ProTX II have similar sequence but have an impact on differ...

Aggregates generated by probabilistic diffusion are fractals reminiscent of the deterministically generated Julia sets: the growth measure of the aggregate is equivalent to the «electric field» around the Julia set and both fractals have a characteristic hairy structure with the fields diverging at the tips. We conjecture that their ftr1.) spectra share the same qualitative features. For Julia ...

“The period comprising the summer, autumn, and winter of 1975/1976 was one of the most exciting times in the life of our laboratory’ in Beckenham. We had been chiefly dedicated to work on inflammation for several of the preceding years, but in July 1976 at the International Congress on Prostaglandins in Florence, Bengt Samuelsson announced the structure of the elusive rabbit aorta contracting s...

ERS HelenW.Belding,M.D., Winston-Salem.N.C. Conrad Maier, M.D., Zurich, Switzerland Sheila T. Callender, M.D., Oxford, England Milo Xetou ek,M.D., Praha, Czechoslovakia Robert B. Chodos, M.D., Franninghain, Mass. Charles E. Rath, M.D., Washington Roger C. Crafts, Ph.D., Cincinnati Jean P. Soulier, M.D., Paris, France C. R. DasGupta, M.D ., Calcutta, India Ram#{243}n M. Su#{225}rez,M.D.,SanJuan,...

We describe examples of rational maps which are not topologically conjugate to a polynomial and whose Julia sets are connected but not locally connected. Introduction and motivations The dynamics of a rational map f acting on Ĉ is concentrated on its Julia set which is (by definition) the minimal compact set invariant by f and f−1 containing at least three points. The question of local connecti...