91. 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.

92. Jacek Guzik, Uros Seljak
Galaxy-dark matter correlations applied to galaxy-galaxy lensing: predictions from the semi-analytic galaxy formation models
MNRAS, vol. 321, p. 439 (2001).
[preprint] [journal]

Abstract:

93. 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

94. 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.

95. Jacek Guzik, Uros Seljak, Matias Zaldarriaga
Lensing effect on polarization in microwave background: extracting convergence power spectrum
Phys.Rev. D, vol. 62, p. 043517 (2000).
[preprint] [journal]

Abstract:

96. Grazyna Siemieniec-Ozieblo, Andrzej Woszczyna
Order reduction in semiclassical cosmology
Phys. Rev. D, vol. 59, p. 083504 (1999).
[abstract] [preprint] [journal]

Abstract:
We investigate the Robertson-Walker cosmology with Lagrangian $R+\alpha_1\hbar R^2+\alpha_2\hbar R^{\mu\nu}R_{\mu\nu} +L_{rad}$ where $L_{rad}$ means classical source with traceless energy-momentum tensor. We weaken the self-consistence condition (L. Parker, J. Z. Simon, Phys. Rev. {D47}(1993),{1339}). Quantum corrections are expressed as contributions to the effective equation of state. We show that the empty space-time is stable within the class of radiation-filled expanding universes with no order reduction of the field equations.