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

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Measurement of the Top Quark Mass Using Dilepton Events

The D0 collaboration has performed a measurement of the top quark mass based on six candidate events for the process t tbar -> b W+ bbar W-, where the W bosons decay to e nu or mu nu. This sample was collected during an exposure of the D0 detector to an integrated luminosity of 125 pb^-1 of sqrt(s)=1.8 TeV p-pbar collisions. We obtain mt = 168.4 +- 12.3 (stat) +- 3.7 (sys) GeV/c^2, consistent with the measurement obtained using single-lepton events. Combination of the single-lepton and dilepton results yields mt = 172.0 +- 7.5 GeV/c^2.Comment: 12 pages, 3 figure

Direct Measurement of the Top Quark Mass at D0

We determine the top quark mass m_t using t-tbar pairs produced in the D0 detector by \sqrt{s} = 1.8 TeV p-pbar collisions in a 125 pb^-1 exposure at the Fermilab Tevatron. We make a two constraint fit to m_t in t-tbar -> b W^+bbar W^- final states with one W boson decaying to q-qbar and the other to e-nu or mu-nu. Likelihood fits to the data yield m_t(l+jets) = 173.3 +- 5.6 (stat) +- 5.5 (syst) GeV/c^2. When this result is combined with an analysis of events in which both W bosons decay into leptons, we obtain m_t = 172.1 +- 5.2 (stat) +- 4.9 (syst) GeV/c^2. An alternate analysis, using three constraint fits to fixed top quark masses, gives m_t(l+jets) = 176.0 +- 7.9 (stat) +- 4.8 (syst) GeV/C^2, consistent with the above result. Studies of kinematic distributions of the top quark candidates are also presented.Comment: 43 pages, 53 figures, 33 tables. RevTeX. Submitted to Phys. Rev.

Search for First Generation Scalar Leptoquark Pairs in ppbar Collisions at sqrt(s)=1.8 TeV

We have searched for first generation scalar leptoquark (LQ) pairs in the enu+jets channel using ppbar collider data (integrated luminosity= 115 pb^-1) collected by the DZero experiment at the Fermilab Tevatron during 1992-96. The analysis yields no candidate events. We combine the results with those from the ee+jets and nunu+jets channels to obtain 95% confidence level (CL) upper limits on the LQ pair production cross section as a function of mass and of beta, the branching fraction to a charged lepton. Comparing with the next-to-leading order theory, we set 95% CL lower limits on the LQ mass of 225, 204, and 79 GeV/c^2 for beta=1, 1/2, and 0, respectively.Comment: 14 pages, 4 figures, submitted to Physical Review Letters Replaced to correct visitor addresse

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

Measurement of Dijet Angular Distributions and Search for Quark Compositeness

We have measured the dijet angular distribution in $\sqrt{s}$=1.8 TeV $p\bar{p}$ collisions using the D0 detector. Order $\alpha^{3}_{s}$ QCD predictions are in good agreement with the data. At 95% confidence the data exclude models of quark compositeness in which the contact interaction scale is below 2 TeV.Comment: 11 pages, Latex, 3 postscript figure

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

Measurement of the Top Quark Pair Production Cross Section in pbarp Collisions

We present a measurement of the ttbar production cross section in ppbar collisions at root(s) = 1.8TeV by the D0 experiment at the Fermilab Tevatron. The measurement is based on data from an integrated luminosity of approximately 125 pb^-1 accumulated during the 1992-1996 collider run. We observe 39 ttbar candidate events in the dilepton and lepton+jets decay channels with an expected background of 13.7+-2.2 events. For a top quark mass of 173.3GeV/c^2, we measure the ttbar production cross section to be 5.5+-1.8 pb.Comment: 11 pages with 3 encapsulated PostScript figures and 2 PostScript table included in the body of the articl