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Titlebook: Deterministic Chaos in General Relativity; David Hobill,Adrian Burd,Alan Coley Book 1994 Springer Science+Business Media New York 1994 cha

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发表于 2025-3-21 17:43:48 | 显示全部楼层 |阅读模式
书目名称Deterministic Chaos in General Relativity
编辑David Hobill,Adrian Burd,Alan Coley
视频video
丛书名称NATO Science Series B:
图书封面Titlebook: Deterministic Chaos in General Relativity;  David Hobill,Adrian Burd,Alan Coley Book 1994 Springer Science+Business Media New York 1994 cha
描述Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com­ plex nonlinear systems that cannot be broken down into the behavior of their con­ stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many
出版日期Book 1994
关键词chaos; dynamical systems; dynamische Systeme; geometry; numerical methods
版次1
doihttps://doi.org/10.1007/978-1-4757-9993-4
isbn_softcover978-1-4757-9995-8
isbn_ebook978-1-4757-9993-4Series ISSN 0258-1221
issn_series 0258-1221
copyrightSpringer Science+Business Media New York 1994
The information of publication is updating

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https://doi.org/10.1007/978-3-319-10503-1en a perturbation is added to the system. By using the Melnikov method for detecting homoclinic chaos in near integrable systems, we conclude that, as one adds a time-periodic perturbation to the static black hole, a region of chaotic motion replaces the homoclinic orbit.
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On Defining Chaos in the Absence of Timed could be quite misleading. In particular, for any integer . > 1 we give an example of a completely integrable .-degree of freedom Hamiltonian system, with compact energy surfaces, having the property that the induced flows on almost all energy surfaces admit sensitive dependence on initial conditions.
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Particle Motion Around Perturbed Black Holes: The Onset of Chaosen a perturbation is added to the system. By using the Melnikov method for detecting homoclinic chaos in near integrable systems, we conclude that, as one adds a time-periodic perturbation to the static black hole, a region of chaotic motion replaces the homoclinic orbit.
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Critical Behaviour in Scalar Field Collapseack hole to spacetimes which do. The near critical regime, . ≈ .*, is characterized by a variety of non-linear phenomena including exponential sensitivity to initial conditions, scale-periodicity, and universal power-law dependence of black hole mass on parameter-space displacement |. − .*|.
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Homoclinic Chaos in Relativistic Cosmologyone where the Universe may be described as a Hamiltonian dynamical system, and other where this is not possible, due to the presence of viscous matter. The overall implications of Chaos for Cosmology and General Relativity are discussed.
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Classical and Quantum Chaos in Robertson-Walker Cosmologiesound the chaotic nucleus of the universe. On the quantum level we discuss particle creation, backscattering, anisotropy in the microwave background, parity violation and how all this relates to the multiple connectivity of the open spacelike slices.
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