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  • 1
    Electronic Resource
    Electronic Resource
    The general exact bijective continuous solution of Feigenbaum's functional equation (1983)
    Springer
    Communications in mathematical physics 91 (1983), S. 431-443 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Solutionsf:ℝ→ℝ of Feigenbaum's functional equationf(f(x))=α−1 f(αx), where α≠0 is a fixed real number, account for many of the fascinating properties of the behaviour of successive iterates of (one parameter families of) nonlinear maps. In connection with the phenomenon of intermittency, interesting families of exact solutions have recently been found (for α〉0). These solutions can all be derived from continuous bijective solutions which are topologically equivalent to translations. In this paper, thegeneral exact continuous bijective solution is found for any α≠0, positive or negative. In particular, it is shown that, forany α≠0, there are solutions which areinequivalent to translations. And it is shown that bijective solutions equivalent to translations exist only when 0〈α〈1. These results considerably enlarge the stock of available exact solutions of Feigenbaum's equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01208784
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  • 2
    Electronic Resource
    Electronic Resource
    A high abundance of massive galaxies 3–6 billion years after the Big Bang (2004)
    [s.l.] : Macmillian Magazines Ltd.
    Nature 430 (2004), S. 181-184 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Hierarchical galaxy formation is the model whereby massive galaxies form from an assembly of smaller units. The most massive objects therefore form last. The model succeeds in describing the clustering of galaxies, but the evolutionary history of massive galaxies, as revealed by their visible ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/nature02667
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  • 3
    Electronic Resource
    Electronic Resource
    EROS AND FAINT RED GALAXIES (2004)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Astronomy and Astrophysics 42 (2004), S. 477-515 
    Details
    ISSN: 0066-4146
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Physics
    Notes: This chapter reviews the properties of faint IR-selected field galaxies and the extremely red color-selected populations in particular. These populations are a mix of passively evolving stellar systems and heavily obscured star-forming galaxies. The star-forming component appears to constitute 20-50% of the population depending on the magnitude and color cuts employed. The remaining objects are a mix of passively evolving ellipticals and early-type disk galaxies. The passively evolving red galaxies are strongly clustered in space and are likely the high-mass high-luminosity end of the elliptical galaxy progenitor population at redshifts between one and two. These galaxies have masses and space densities that appear to be in conflict with late-forming hierarchical galaxy-formation models. The red galaxies appear to be a population that is distinct from the moderately star-forming Lyman-Break galaxies but may be related to the starburst population at z 〉 2 seen in deep submillimeter surveys.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.astro.42.053102.134032
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  • 4
    Electronic Resource
    Electronic Resource
    A finsler perturbation of the Poincaré metric (1993)
    Springer
    General relativity and gravitation 25 (1993), S. 179-187 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract One method of gaining some insight into Finsler geomety is that of studying small Finsler perturbations of Riemannian metrics. We consider here the the standard two-dimensional upper half plane Poincaré metric, for which the geodesics are semi-circles and vertical lines. The effect of a simple Finsler perturbation on these geodesics is given by an explicit computation of the perturbed geodesics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00758825
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  • 5
    Electronic Resource
    Electronic Resource
    The general four-dimensional spherically symmetric Finsler space (1993)
    Springer
    General relativity and gravitation 25 (1993), S. 589-602 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Finsler geometries give natural generalisations of Riemannian geometries, and hence possible natural extensions of general relativity. In this latter (gravitational) context, it is of particular interest to find the general spherically symmetric Finsler metric on ℝ4. In this paper, we derive this metric. The general solution is given in two alternative forms, the second of which allows easy comparison with Riemannian-like metrics. We also derive the general axially symmetric Finsler metric on ℝ4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00757070
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  • 6
    Electronic Resource
    Electronic Resource
    Some linear Bäcklund transformations (1980)
    Springer
    Letters in mathematical physics 4 (1980), S. 39-43 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Dirac's equation is a first-order auto-Bäcklund transformation for the Klein-Gordon equation in 4 variables, this equation being second-order in each of the 4 variables. Here first-order auto-Bäcklund transformations are given for any linear equation of arbitrary (possibly different) order in each of n variables (n arbitrary). This class of equations includes, for example, any of the linearised versions of the KdV hierarchy or equations, and the n-dimensional diffusion equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00419803
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  • 7
    Electronic Resource
    Electronic Resource
    Existence of strong Bäcklund transformations in four or more dimensions and generalization of a family of Bäcklund transformations (1978)
    Springer
    Letters in mathematical physics 2 (1978), S. 493-498 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A Bäcklund transformation between two (sets of) differential equations is strong if the transformation equations already imply the two equations. For each dimension n=2 k , k⩾1, the existence of such strong transformations is proved by constructing a wide variety of them. A simple generalization of a known family of Bäcklund transformations is also given. One such provides a useful analogy for Yang's ‘instanton’ equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398502
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  • 8
    Electronic Resource
    Electronic Resource
    Rational parametrisation of normalised stiefel manifolds, and explicit non-'t hooft solutions of the Atiyah-Drinfeld-Hitchin-Manin instanton matrix equations for Sp(n) (1981)
    Springer
    Letters in mathematical physics 5 (1981), S. 255-261 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is proved that normalised Stiefel manifolds admit a rational parametrisation which generalises Cayley's parametrisation of the unitary groups. Applying (the quaternionic case of) this parametrisation to the Atiyah-Drinfeld-Hitchin-Manin (ADHM) instanton matrix equations, large families of new explicit rational solutions emerge. In particular, new explicit non-'t Hooft solutions are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00401473
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  • 9
    Electronic Resource
    Electronic Resource
    Bäcklund transformations as nonlinear Dirac equations (1977)
    Springer
    Letters in mathematical physics 2 (1977), S. 167-170 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is pointed out that the Bäcklund transformations for a physically interesting class of nonlinear partial differential equations can be interpreted as generalisations of the Cauchy Riemann equations or as nonlinear Dirac equations. The generalisations are inhomogenisations of the Cauchy Riemann equations (or their hyperbolic analogue), whose condensed form makes the transformations easy to remember, which suggests ways to generalise to more than 2 dimensions, and which suggest that complex analysis techniques may be helpful in understanding the transformations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398583
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  • 10
    Electronic Resource
    Electronic Resource
    Ultrageneralised complex analysis (1980)
    Springer
    Letters in mathematical physics 4 (1980), S. 509-514 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The zero rest mass Euclidean Dirac equations in 2 (4) dimensions may be regarded as ‘square roots’ of the second order harmonic equation, and give rise to the crucial integral theorem and integral formula of complex (quaternionic) analysis. Recently discovered ‘2rth root’ equations for the 2rth order ‘harmonic’ equations are here shown to give rise to a similar integral theorem and integral formula.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00943438
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