Department of Relativistic Astrophysics and Cosmology
 
 
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25. P. Bizoń, S. J. Szybka, A. Wassserman
Periodic self-similar wave maps coupled to gravity
Phys. Rev. D, vol. 69, p. 064014 (2004).
[abstract] [preprint] [journal]

Abstract:
We continue our studies of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. Using mixed numerical and analytical methods we show existence of an unstable periodic solution lying at the boundary between the basins of two generic attractors.

26. S. J. Szybka
Chaotic self-similar wave maps coupled to gravity
Phys. Rev. D, vol. 69, p. 084014 (2004).
[abstract] [preprint] [journal]

Abstract:
We continue our studies of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. For some values of the coupling constant we present numerical evidence for the chaotic solution and the fractal threshold behavior. We explain this phenomenon in terms of horseshoe-like dynamics and heteroclinic intersections.

27. 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.

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