8,630 research outputs found

    Renormalization in the Henon family, I: universality but non-rigidity

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    In this paper geometric properties of infinitely renormalizable real H\'enon-like maps FF in R2\R^2 are studied. It is shown that the appropriately defined renormalizations RnFR^n F converge exponentially to the one-dimensional renormalization fixed point. The convergence to one-dimensional systems is at a super-exponential rate controlled by the average Jacobian and a universal function a(x)a(x). It is also shown that the attracting Cantor set of such a map has Hausdorff dimension less than 1, but contrary to the one-dimensional intuition, it is not rigid, does not lie on a smooth curve, and generically has unbounded geometry.Comment: 42 pages, 5 picture

    The multipliers of periodic points in one-dimensional dynamics

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    It will be shown that the smooth conjugacy class of an SS-unimodal map which does not have a periodic attractor neither a Cantor attractor is determined by the multipliers of the periodic orbits. This generalizes a result by M.Shub and D.Sullivan for smooth expanding maps of the circle

    Basins of Attraction for Chimera States

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    Chimera states---curious symmetry-broken states in systems of identical coupled oscillators---typically occur only for certain initial conditions. Here we analyze their basins of attraction in a simple system comprised of two populations. Using perturbative analysis and numerical simulation we evaluate asymptotic states and associated destination maps, and demonstrate that basins form a complex twisting structure in phase space. Understanding the basins' precise nature may help in the development of control methods to switch between chimera patterns, with possible technological and neural system applications.Comment: Please see Ancillary files for the 4 supplementary videos including description (PDF

    The impact of heat waves and cold spells on mortality rates in the Dutch population.

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    We conducted the study described in this paper to investigate the impact of ambient temperature on mortality in the Netherlands during 1979-1997, the impact of heat waves and cold spells on mortality in particular, and the possibility of any heat wave- or cold spell-induced forward displacement of mortality. We found a V-like relationship between mortality and temperature, with an optimum temperature value (e.g., average temperature with lowest mortality rate) of 16.5 degrees C for total mortality, cardiovascular mortality, respiratory mortality, and mortality among those [Greater and equal to] 65 year of age. For mortality due to malignant neoplasms and mortality in the youngest age group, the optimum temperatures were 15.5 degrees C and 14.5 degrees C, respectively. For temperatures above the optimum, mortality increased by 0.47, 1.86, 12.82, and 2.72% for malignant neoplasms, cardiovascular disease, respiratory diseases, and total mortality, respectively, for each degree Celsius increase above the optimum in the preceding month. For temperatures below the optimum, mortality increased 0.22, 1.69, 5.15, and 1.37%, respectively, for each degree Celsius decrease below the optimum in the preceding month. Mortality increased significantly during all of the heat waves studied, and the elderly were most effected by extreme heat. The heat waves led to increases in mortality due to all of the selected causes, especially respiratory mortality. Average total excess mortality during the heat waves studied was 12.1%, or 39.8 deaths/day. The average excess mortality during the cold spells was 12.8% or 46.6 deaths/day, which was mostly attributable to the increase in cardiovascular mortality and mortality among the elderly. The results concerning the forward displacement of deaths due to heat waves were not conclusive. We found no cold-induced forward displacement of deaths