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  • 1
    Electronic Resource
    Electronic Resource
    Goodstein algorithm as a super-transient dynamical system
    Amsterdam : Elsevier
    Physics Letters A 180 (1993), S. 83-86 
    Details
    ISSN: 0375-9601
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0375-9601(93)90498-O
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  • 2
    Electronic Resource
    Electronic Resource
    Cosmological models expressible as gradient vector fields (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 858-873 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Classes of cosmological models, for which Einstein's equations reduce to two-dimensional dynamical systems, are studied in the presence of stochastic perturbations using the steady state of the associated Fokker–Planck equations and Zeeman's notion of ε-stability. In all cases, a set of variables is found for which the dynamical systems are expressible as gradient vector flows, showing that the associated cosmologies are stochastically stable. Such models are also important in connection with application of catastrophy theory to cosmology. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531416
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  • 3
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    Fragility and Deterministic Modelling in the Exact Sciences (1991)
    Oxford : Periodicals Archive Online (PAO)
    The British journal for the philosophy of science. 42:2 (1991:June) 147 
    Details
    ISSN: 0007-0882
    Topics: Natural Sciences in General , Philosophy
    URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pao:&rft_dat=xri:pao:article:4064-1991-042-02-000001
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  • 4
    Electronic Resource
    Electronic Resource
    Is the Sun almost-intransitive? (1978)
    [s.l.] : Nature Publishing Group
    Nature 276 (1978), S. 802-803 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] A radically different hypothesis by Lorenz, suggests that the climatic variability over some time scales may turn out to be non-deterministic14-16. This possibility arises, essentially, from the fact that the climate can be defined as a set of long-term statistics of the time-dependent solution of ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/276802a0
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  • 5
    Electronic Resource
    Electronic Resource
    Topology and Fragility in Cosmology (1998)
    Springer
    General relativity and gravitation 30 (1998), S. 535-543 
    Details
    ISSN: 1572-9532
    Keywords: COSMOLOGY ; TOPOLOGY ; CHAOTIC MIXING ; FRAGILITY
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We introduce the notion of topological fragility and briefly discuss some examples from the literature. An important example of this type of fragility is the way globally anisotropic Bianchi V generalisations of the FLRW k = −1 model result in a radical restriction on the allowed topology of spatial sections, thereby excluding compact cosmological models with negatively curved three-sections with anisotropy. An outcome of this is to exclude chaotic mixing in such models, which may be relevant, given the many recent attempts at employing compact FLRW k = −1 models to produce chaotic mixing in the cosmic microwave background radiation, if the Universe turns out to be globally anisotropic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018809922606
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  • 6
    Electronic Resource
    Electronic Resource
    Conventionalism and general relativity (1978)
    Springer
    Foundations of physics 8 (1978), S. 229-237 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We argue that the geometry of spacetime is a convention that can be freely chosen by the scientist; no experiment can ever determine this geometry of spacetime, only the behavior of matter in space and time. General relativity is then rewritten in terms of an arbitrary conventional geometry of spacetime in which particle trajectories are determined by forces in that geometry, and the forces determined by fields produced by sources in that geometry. As an example, we consider radial trajectories in the field of a single particle expressed in the spacetime of special relativity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00715209
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  • 7
    Electronic Resource
    Electronic Resource
    Non-Riemann geometrizable effects in the gravitational one-body problem (1979)
    Springer
    General relativity and gravitation 10 (1979), S. 307-312 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the question of whether the “correct” theory of gravity is a metric theory. The metric hypothesis is shown to place severe restrictions on the form of the equation of motion for the one-body problem. By relaxing these restrictions we include nonmetric contributions to the equation of motion, and the solution in the post-Newtonian approximation is given. The solution given here contains five arbitrary parameters in place of the usual two (β, γ) of metric theories. One of them produces a secular change in the eccentricity; the others contribute to the perihelion advance and to periodic terms. Only certain combinations of these parameters can be determined even from orbits with different eccentricities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00759488
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  • 8
    Electronic Resource
    Electronic Resource
    Viability criteria for the theories of gravity and finsler spaces (1986)
    Springer
    General relativity and gravitation 18 (1986), S. 849-859 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is commonly held that the Riemannian geometry adopted as the theoretical framework within which observations and experiments, concerning the ‘correct’ theory of gravity, are analyzed is the most general ‘viable’ geometry consistent with observed phenomena. This viewpoint is further strengthened by the belief that the projective and the conformal structures of the space-time together with an additional assumption concerning the constancy of the norm of vectors under parallel transport would uniquely determine its underlying geometry to be Riemannian. We show here that a more general geometrical framework due to Finsler can be made compatible with these structures and still remain non-Riemannian. The potential importance of this result in connection with developing and testing alternative theories of gravity is briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00770205
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  • 9
    Electronic Resource
    Electronic Resource
    Fragility in cosmology (1992)
    Springer
    General relativity and gravitation 24 (1992), S. 835-855 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An important implicit assumption usually made regarding the nature of the cosmos and the theoretical framework employed in its study is that of structural stability. On the basis of the modern results in dynamical systems theory, it has recently been argued that the appropriate theoretical framework might instead turn out to be that of structural fragility. Here we give further examples and review the major results in cosmology to illustrate the potential extent of the relevance of fragility in cosmology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00759090
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  • 10
    Electronic Resource
    Electronic Resource
    Redistribution of energy by vertical oscillations in the solar atmosphere (1981)
    Springer
    Solar physics 71 (1981), S. 203-213 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The effect of vertical oscillations with periods between 90 s and 300 s on a solar atmosphere governed by heat conduction and radiation loss is examined. The effect is found to be primarily a redistribution, rather than a net addition or subtraction, of energy within the low corona, mainly by long period (180 to 300 s) oscillations. The redistribution of energy is found to affect the time-averaged temperature and density profiles of such an atmosphere, particularly in the low corona. The amount of energy redistributed is found to increase with increasing period.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00167544
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