Periodic attractors of perturbed one-dimensional maps

In this paper we investigate how many periodic attractors maps in a small neighbourhood of a given map can have. For this purpose we develop new tools which help to make uniform cross-ratio distortion estimates in a neighbourhood of a map with degenerate critical points

Cyclicity in families of circle maps

In this paper we will study families of circle maps of the form x↦x+2πr+af(x)(mod2π) and investigate how many periodic trajectories maps from this family can have for a ‘typical’ function f provided the parameter a is small

The dynamics of complex box mappings

In holomorphic dynamics, complex box mappings arise as first return maps to well-chosen domains. They are a generalization of polynomial-like mapping, where the domain of the return map can have infinitely many components. They turned out to be extremely useful in tackling diverse problems. The purpose of this paper is: -To illustrate some pathologies that can occur when a complex box mapping is not induced by a globally defined map and when its domain has infinitely many components, and to give conditions to avoid these issues. -To show that once one has a box mapping for a rational map, these conditions can be assumed to hold in a very natural setting. Thus we call such complex box mappings dynamically natural. -Many results in holomorphic dynamics rely on an interplay between combinatorial and analytic techniques: (*)the Enhanced Nest by Kozlovski-Shen-van Strien; (*)the Covering Lemma by Kahn-Lyubich; (*)the QC-Criterion, the Spreading Principle. The purpose of this paper is to make these tools more accessible so that they can be used as a 'black box', so one does not have to redo the proofs in new settings. -To give an intuitive, but also rather detailed, outline of the proof of the following results by Kozlovski-van Strien for non-renormalizable dynamically natural box mappings: (*)puzzle pieces shrink to points; (*)topologically conjugate non-renormalizable polynomials and box mappings are quasiconformally conjugate. -We prove the fundamental ergodic properties for dynamically natural box mappings. This leads to some necessary conditions for when such a box mapping supports a measurable invariant line field on its filled Julia set. These mappings are the analogues of Lattes maps in this setting. -We prove a version of Mane's Theorem for complex box mappings concerning expansion along orbits of points that avoid a neighborhood of the set of critical points

Rigidity of escaping dynamics for transcendental entire functions

We prove an analog of Boettcher's theorem for transcendental entire functions in the Eremenko-Lyubich class B. More precisely, let f and g be entire functions with bounded sets of singular values and suppose that f and g belong to the same parameter space (i.e., are *quasiconformally equivalent* in the sense of Eremenko and Lyubich). Then f and g are conjugate when restricted to the set of points which remain in some sufficiently small neighborhood of infinity under iteration. Furthermore, this conjugacy extends to a quasiconformal self-map of the plane. We also prove that this conjugacy is essentially unique. In particular, we show that an Eremenko-Lyubich class function f has no invariant line fields on its escaping set. Finally, we show that any two hyperbolic Eremenko-Lyubich class functions f and g which belong to the same parameter space are conjugate on their sets of escaping points.Comment: 28 pages; 2 figures. Final version (October 2008). Various modificiations were made, including the introduction of Proposition 3.6, which was not formally stated previously, and the inclusion of a new figure. No major changes otherwis

Complex bounds for multimodal maps: bounded combinatorics

We proved the so called complex bounds for multimodal, infinitely renormalizable analytic maps with bounded combinatorics: deep renormalizations have polynomial-like extensions with definite modulus. The complex bounds is the first step to extend the renormalization theory of unimodal maps to multimodal maps.Comment: 20 pages, 3 figure

Complex maps without invariant densities

We consider complex polynomials $f(z) = z^\ell+c_1$ for $\ell \in 2\N$ and $c_1 \in \R$, and find some combinatorial types and values of $\ell$ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when $\ell$ sufficiently large and also for a class of `long-branched' maps of any critical order.Comment: Typos corrected, minor changes, principally to Section

Search for Top Squark Pair Production in the Dielectron Channel

This report describes the first search for top squark pair production in the channel stop_1 stopbar_1 -> b bbar chargino_1 chargino_1 -> ee+jets+MEt using 74.9 +- 8.9 pb^-1 of data collected using the D0 detector. A 95% confidence level upper limit on sigma*B is presented. The limit is above the theoretical expectation for sigma*B for this process, but does show the sensitivity of the current D0 data set to a particular topology for new physics.Comment: Five pages, including three figures, submitted to PRD Brief Report

Search for a Fourth Generation Charge -1/3 Quark via Flavor Changing Neutral Current Decay

We report on a search for pair production of a fourth generation charge -1/3 quark (b') in pbar p collisions at sqrt(s) = 1.8 TeV at the Fermilab Tevatron using an integrated luminosity of 93 pb^-1. Both quarks are assumed to decay via flavor changing neutral currents (FCNC). The search uses the signatures gamma + 3 jets + mu-tag and 2 gamma + 2 jets. We see no significant excess of events over the expected background. We place an upper limit on the production cross section times branching fraction that is well below theoretical expectations for a b' quark decaying exclusively via FCNC for b' quark masses up to m(Z) + m(b).Comment: Eleven pages, two postscript figures, submitted to Physical Review Letter

Search for W~1Z~2\widetilde{W}_1\widetilde{Z}_2 Production via Trilepton Final States in ppˉp\bar{p} collisions at s=1.8\sqrt{s}=1.8 TeV

We have searched for associated production of the lightest chargino, $\widetilde{W}_1$, and next-to-lightest neutralino, $\widetilde{Z}_2$, of the Minimal Supersymmetric Standard Model in $p\bar{p}$ collisions at \mbox{$\sqrt{s}$ = 1.8 TeV} using the \D0 detector at the Fermilab Tevatron collider. Data corresponding to an integrated luminosity of 12.5$\pm 0.7$ \ipb were examined for events containing three isolated leptons. No evidence for $\widetilde{W}_1\widetilde{Z}_2$ pair production was found. Limits on $\sigma(\widetilde{W}_1\widetilde{Z}_2)$Br$(\widetilde{W}_1\to l\nu\widetilde{Z}_1)$Br$(\widetilde{Z}_2\to l\bar{l}\widetilde{Z}_1)$ are presented.Comment: 17 pages (13 + 1 page table + 3 pages figures). 3 PostScript figures will follow in a UUEncoded, gzip'd, tar file. Text in LaTex format. Submitted to Physical Review Letters. Replace comments - Had to resumbmit version with EPSF directive

Measurement of the WW Boson Mass

A measurement of the mass of the $W$ boson is presented based on a sample of 5982 $W \rightarrow e \nu$ decays observed in $p\overline{p}$ collisions at $\sqrt{s}$ = 1.8~TeV with the D\O\ detector during the 1992--1993 run. From a fit to the transverse mass spectrum, combined with measurements of the $Z$ boson mass, the $W$ boson mass is measured to be $M_W = 80.350 \pm 0.140 (stat.) \pm 0.165 (syst.) \pm 0.160 (scale) GeV/c^2$.Comment: 12 pages, LaTex, style Revtex, including 3 postscript figures (submitted to PRL