Related papers: The Mixmaster Cosmological Model as a Pseudo-Eucli…
The problem of integrability of the mixmaster model as a dynamical system with finite degrees of freedom is investigated. The model belongs to the class of pseudo-Euclidean generalized Toda chains. It is presented as a quasi-homogeneous…
We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case…
We propose deep Koopman-layered models with learnable parameters in the form of Toeplitz matrices for analyzing the transition of the dynamics of time-series data. The proposed model has both theoretical solidness and flexibility. By virtue…
We consider an integrable three-dimensional system of ordinary differential equations introduced by S.V. Kovalevskaya in a letter to G. Mittag-Leffler. We prove its isomorphism with the three-dimensional Euler top, and propose two…
The integration procedure for multidimensional cosmological models with multicomponent perfect fluid in spaces of constant curvature is developed. Reduction of pseudo-Euclidean Toda-like systems to the Euclidean ones is done. Some known…
The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the ``singularity'' is reduced to a billiard on the…
We consider a D-dimensional cosmological model describing an evolution of (n+1) Einstein factor spaces in the theory with several dilatonic scalar fields and generalized electro-magnetic forms, admitting an interpretation in terms of…
The Bianchi IX cosmological model is analyzed in a generalized uncertainty principle framework. The Arnowitt-Deser-Misner reduction of the dynamics is performed and a time-coordinate, namely the volume of the Universe, naturally arises.…
We explore various aspects of the correspondence between dimer models and integrable systems recently introduced by Goncharov and Kenyon. Dimer models give rise to relativistic integrable systems that match those arising from 5d N=1 gauge…
A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…
The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions which may be written in closed form are isolated with the…
The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions which may be written in closed form are isolated with the…
The purpose of this material is to review the Adler Kostant Symes scheme as a theory which can be developped succesfully in different contexts. It was useful to describe some mechanical systems, the so called generalized Toda, and now it…
We analyze the semiclassical polymer dynamics of the inhomogeneous Mixmaster model by choosing the cubed scale factor as the discretized configurational variable, while the anisotropies remain pure Einsteinian variables. Such a modified…
In this work, we examine the dynamical aspects of the cosmological Mixmaster model within the framework of non-commutative generalized uncertainty principle (GUP) theories. The theory is formulated classically by introducing a well-defined…
The Toda chain is the prime example of a classical integrable system with strictly local conservation laws. Relying on the Dumitriu-Edelman matrix model, we obtain the generalized free energy of the Toda chain and thereby establish a…
This paper begins with a short presentation of the Bianchi IX or ``Mixmaster'' cosmological model, and some ways of writing the Einstein equations for it. There is then an interlude describing how I came to a study of this model, and then a…
In this paper, we study the well-posedeness at low regularity of a two-dimensional system obtained as a reduced model for micropolar fluid dynamics. At the mathematical level, the system presents a coupling between an Euler-type equation…
A model of multidimensional mixmaster-type vacuum universe is considered. It belongs to a class of pseudo-Euclidean chains characterized by root vectors. An algebraic approach of our investigation is founded on construction of Cartan matrix…
Dyadic models of the Euler equations were introduced as toy models to study the behaviour of an inviscid fluid in turbulence theory. In 1974 Novikov proposed a generalized mixed dyadic model that extends both Katz-Pavlovic and Obukhov…