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Abstract: It was shown, in our previous works, that periodic points of $d$ dimensional rational integrable maps form varieties if the number of invariants $p$ is greater than $d/2$. In the case of 3 d...
Classical generalization of general relativity is considered as gravitational alternative for unified description of the early-time inflation with late-time cosmic acceleration. The structure and cosm...
The non-linear evolution of the halo population is followed by solving the continuity equation under the hypothesis that haloes move by the action of gravity. An exact and general formula for the Eule...
We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interfa...
A quartic, self-interacting potential in the induced gravity framework is known to have a pure de Sitter attractor for the homogeneous mode. In order to obtain non-zero slow roll parameters we theref...
This thesis includes several original results. All of them are already published or submitted for publication. I present here the short summary of main results: The ultraviolet singular structure of t...
The current status of the recent developments of the second-order gauge-invariant cosmological perturbation theory is reviewed. To show the essence of this perturbation theory, we concentrate only on ...

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