Related papers: On dynamical Teichmuller spaces
Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…
This text reviews certain notions in metric geometry that may have further applications to problems in complex geometry and holomorphic dynamics in several variables. The discussion contains a few unrecorded results and formulates a number…
This paper surveys results found by the authors in the previous papers (see for example, A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of a viscid fluid, Journal of Geometry and Physics, 130,…
We define a kind of moduli space of nested surfaces and mappings, which we call a comparison moduli space. We review examples of such spaces in geometric function theory and modern Teichmueller theory, and illustrate how a wide range of…
We suggest a way to associate to a rational map of the Riemann sphere a three dimensional object called a hyperbolic orbifold 3-lamination. The relation of this object to the map is analogous to the relation of a hyperbolic 3-manifold to a…
After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
We compare the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones by a very elementary approach. The comparison gives some conditions, which are easy to verify for a given Lie algebra, for deciding…
A deformation of the Fock space based on the finite difference replacement for the derivative is introduced. The deformation parameter is related to the dimension of the finite analogue of the Fock space.
This paper introduces indefinite proximities inherent in the collection of physical objects found in a dynamical system. Axiomatically, these indefinite proximities lead to a new form of Hausdorff topology, which is indefinite…
Diffusion metamaterials with artificial spatial structures have significant potential in controlling energy and mass transfer. Those static structures may lead to functionality and tunability constraints, impeding the application scope of…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
This set of lecture notes gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations. Later sections describe more advanced…
A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different…
Some special solutions to the reflection equation are considered. These boundary matrices are defined on the common quantum space with the other operators in the chain. The relations with the Drinfeld twist are discussed.
We provide a comprehensive account of prethermal discrete time crystals within classical Hamiltonian dynamics, complementing and extending our recent work [Phys. Rev. Lett. 127, 140602 (2021)]. Considering power-law interacting spins on…
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical…
We study expansive dynamical systems from the viewpoint of general topology. We introduce the notions of orbit and refinement expansivity on topological spaces extending expansivity in the compact metric setting. Examples are given on…
We lay foundations of the subject in the title, on which we build in another paper devoted to isometries in spaces of K\"ahler metrics.
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…