Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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16 Dec 1998TL;DR: In this article, a generalized Liapunov theorem was proposed to guarantee practical asymptotic stability for periodic solutions of time-invariant systems in terms of the Poincare map.
Abstract: We prove a generalized Liapunov theorem which guarantees practical asymptotic stability. Based on this theorem, we show that if the averaged system x/spl dot/=f/sub av/(x) corresponding to x/spl dot/=f(x,t) is globally asymptotically stable then, starting from an arbitrarily large set of initial conditions, the trajectories of x/spl dot/=f(x, t//spl epsiv/) converge uniformly to an arbitrarily small residual set around the origin when /spl epsiv/>0 is taken sufficiently small. In other words, the origin is semi-globally practically asymptotically stable. As another application of the generalized Liapunov theorem, one may recover the classical asymptotic stability result for periodic solutions of time-invariant systems x/spl dot/=f(x) in terms of the Poincare map.
17 citations
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17 citations
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TL;DR: In this paper, the authors studied the possibility of defining a Hilbert space for n=(d+1)-dimensional general relativity in some asymptotic regions of Wheeler's superspace.
Abstract: The author studies the possibility of defining a Hilbert space for n=(d+1)-dimensional general relativity in some asymptotic regions of Wheeler's superspace. The author distinguishes two asymptotic regions: (i) the 'classical asymptotic region', which contains geometries with a volume much larger than the Planck volume and (ii) the 'quantum asymptotic region', which contains geometries with a volume much smaller than the Planck volume. It is shown that for n>or=4 one can define a Hilbert space only in the classical asymptotic region of superspace, while for n(4 one can define a Hilbert space in the quantum asymptotic region or in the classical asymptotic region, but not both. It is argued that in a good theory of quantum gravity one should be able to define a Hilbert space in the two asymptotic regions. Therefore it seems that Einstein's general relativity is not a good candidate for a quantum theory of gravitation. But it (the 3+1)-dimensional case) can be a good classical limit of that theory. The above criterion can serve in the search for a quantum theory of gravitation.
17 citations
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TL;DR: The asymptotic forms of bounds on the information rate ofLee-codes are derived and their relative strength is discussed and it is shown that the covering radius of Lee-codes lies asymPTotically on the Varshamov-Gilbert bound.
17 citations