Expansive homeomorphisms of the plane

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques involve topological and metric aspects of the plane. The use of a Lyapunov metric function which defines the same topology as the one induced by the usual metric but that, in general, is not equivalent to it is an example of such techniques. The discovery of a hypothesis about the behavior of Lyapunov functions at infinity allows us to generalize some results that are valid in the compact context. Additional local properties allow us to obtain another classification theorem.Comment: 29 pages, 22 figure

Topologically anosov plane homeomorphisms

This paper deals with classifying the dynamics of topologically Anosov plane homeomorphisms. We prove that a topologically Anosov homeomorphism f: ℝ2 → ℝ2 is conjugate to a homothety if it is the time one map of a flow. We also obtain results for the cases when the nonwan- dering set of f reduces to a fixed point, or if there exists an open, connected, simply connected proper subset U such that U ⊂ Int(f(U)), and such that ∪n ≥ 0fn(U) = R2.In the general case, we prove a structure theorem for the α-limits of orbits with empty ω-limit (or the ω-limits of orbits with empty α-limit)

Topologically Anosov plane homeomorphisms

This paper deals with classifying the dynamics of {\it Topologically Anosov} plane homeomorphisms. We prove that a Topologically Anosov homeomorphism $f:\mathbb{R}^2 \to \mathbb{R}^2$ is conjugate to a homothety if it is the time one map of a flow. We also obtain results for the cases when the nonwandering set of $f$ reduces to a fixed point, or if there exists an open, connected, simply connected proper subset $U$ such that $U \subset \mathrm{Int}(\overline {f(U)})$, and such that $\cup_{n\geq 0} f^n (U)= \mathbb{R}^2$. In the general case, we prove a structure theorem for the $\alpha$-limits of orbits with empty $\omega$-limit (or the $\omega$-limits of orbits with empty $\alpha$-limit), and we show that any basin of attraction (or repulsion) must be unbounded.Comment: 10 page

Linearization of planar homeomorphisms with a compact attractor

Kerékjártó proved in 1934 that a planar homeomorphism with an asymptotically stable fixed point is conjugated, on its basin of attraction, to one of the maps z (Formula Present.) depending on whether f preserves or reverses the orientation. We extend this result to planar homeomorphisms with a compact attractor

Geographic clusters of congenital anomalies in Argentina

Geographical clusters are defined as the occurrence of an unusual number of cases higher than expected in a given geographical area in a certain period of time. The aim of this study was to identify potential geographical clusters of specific selected congenital anomalies (CA) in Argentina. The cases were ascertained from 703,325 births, examined in 133 maternity hospitals in the 24 provinces of Argentina. We used the spatial scan statistic to determine areas of Argentina which had statistically significant elevations of prevalence. Prenatal diagnosis followed by referral of high-risk pregnancies to high complexity hospitals in a hospital-based surveillance system can create artifactual clusters. We assessed the referral bias by evaluating the prevalence heterogeneity within each cluster. Eight clusters of selected CAs with unusually high birth prevalence were identified: anencephaly, encephalocele, spina bifida, diaphragmatic hernia, talipes equinovarus, omphalocele, Cleft lip with or without cleft palate (CL/P), and Down syndrome. The clusters of Down syndrome and CL/P observed in this study match the previously reported clusters. These findings support local targeted interventions to lower the prevalence of the CAs and/or further research on the cause of each cluster. The clusters of spina bifida, anencephaly, encephalocele, omphalocele, congenital diaphragmatic hernia, and talipes equinovarus may be influenced by prenatal diagnosis and referral to high complexity hospitals.Fil: Groisman, Boris. Ministerio de Salud de la Nación. Centro Nacional de Genética Médica. Registro Nacional de Anomalías Congénitas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gili, Juan Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas "Norberto Quirno". CEMIC-CONICET.; ArgentinaFil: Gimenez, Lucas Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas "Norberto Quirno". CEMIC-CONICET.; ArgentinaFil: Poletta, Fernando Adrián. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas "Norberto Quirno". CEMIC-CONICET.; Argentina. Instituto Nacional de Genética Médica Populacional; BrasilFil: Bidondo, Maria Paz. Ministerio de Salud de la Nación. Centro Nacional de Genética Médica. Registro Nacional de Anomalías Congénitas; Argentina. Universidad de Buenos Aires. Facultad de Medicina; ArgentinaFil: Barbero, Pablo. Ministerio de Salud de la Nación. Centro Nacional de Genética Médica. Registro Nacional de Anomalías Congénitas; ArgentinaFil: Liascovich, Rosa. Ministerio de Salud de la Nación. Centro Nacional de Genética Médica. Registro Nacional de Anomalías Congénitas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: López Camelo, Jorge Santiago. Instituto Nacional de Genética Médica Populacional; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. CEMIC-CONICET. Centro de Educaciones Médicas e Investigaciones Clínicas "Norberto Quirno". CEMIC-CONICET.; Argentin