RESEARCH GROUP

MATHEMATICAL STRUCTURES OF THE UNIVERSE

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91. M. Heller, W. Sasin
Differential Groupoids and Their Application to the Theory of Spacetime Singularities
International Journal of Theoretical Physics, vol. 41, pp. 919-937 (2002).

Abstract:

92. Leszek M. Sokołowski
Quantum spacetime and the problem of time in quantum gravity.
A Synthese Library (Studies in Epistemology, Logic, Methodology and Philosophy of Science), vol. 309, pp. 23-46 (2002).
[abstract]

Abstract:
in: "A Collection of Polish Works on Philosophical Problems of Time and Spacetime", ed. by H. Eilstein, Synthese Library (Studies in Epistemology, Logic, Methodology and Philosophy of Science) vol. 309, Kluwer Acad. Publ., Dordrecht 2002.

93. A. V. Pokrovskii, S. J. Szybka, J. G. McInerney
Topological Degree in Locating Homoclinic Structures for Discrete Dynamical Systems
Izv. Ross. Akad. Estestv. Nauk Mat., vol. 5, pp. 152-183 (2001).
[abstract] [preprint] [journal]

Abstract:
A method of applying topological degree theory to analysis of chaotic behaviour of dynamical systems is described. The scheme combines one suggested by P. Zgliczynski with the method of topological shadowing. As an illustration a Henon mapping with a homoclinic tangency is considered.

94. Zdzislaw A. Golda, Andrzej Woszczyna
Acoustics of early universe. I. Flat versus open universe models
Class. Quant. Grav., vol. 18, pp. 543-554 (2001).
[abstract] [preprint] [journal]

Abstract:
A simple perturbation description unique for all signs of curvature, and based on the gauge-invariant formalisms is proposed to demonstrate that: (1) The density perturbations propagate in the flat radiation-dominated universe in exactly the same way as electromagnetic or gravitational waves propagate in the epoch of the matter domination. (2) In the open universe, sounds are dispersed by curvature. The space curvature defines the minimal frequency $\omega_{\rm c}$ below which the propagation of perturbations is forbidden. Gaussian acoustic fields are considered and the curvature imprint in the perturbations spectrum is discussed

95. Zdzislaw A. Golda, Andrzej Woszczyna
Acoustics of early universe. II. Lifshitz vs. gauge-invariant theories
J. Math. Phys., vol. 42, pp. 856-862 (2001).
[abstract] [preprint] [journal]

Abstract:
Appealing to classical methods of order reduction, we reduce the Lifshitz system to a second order differential equation. We demonstrate its equivalence to well known gauge-invariant results. For a radiation dominated universe we express the metric and density corrections in their exact forms and discuss their acoustic character.

96. M. Heller, W. Sasin, Z. Odrzygóźdź
State Vector Reduction as a Shadow of Noncommutative Dynamics
Journal of Mathematical Physics, vol. 41, pp. 5168-5179 (2000).

Abstract:
Abstract

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