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We study dynamics of the Latt\`es maps in the complex plane in terms of the Cuntz-Krieger algebras associated to the endomorphisms of the non-commutative tori. In particular, it is shown that iterations of the Latt\`es maps can be reduced…
We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between…
Intertwiner is a homomorphism between two existing dynamical R matrices, first introduced by Baxter in eight vertex-SOS correspondence, we develop certain equivalence relations among R matrices using intertwiners. Twist is a homomorphism…
For a rational and $C_2$-cofinite vertex operator algebra $V$ with an automorphism group $G$ of prime order, the fusion rules for twisted $V$-modules are studied, a twisted Verlinde formula which relates fusion rules for $g$-twisted modules…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…
After a short review of the classical Lie theorem, a finite dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a…
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…
In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…
We study new classes of metric transformations in the context of scalar-tensor theories, which involve both higher derivatives of the scalar field and derivatives of the metric itself. In general, such transformations are not invertible as…
The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra which depends on the choice of an auxiliary transversal Dirac structure; if the transversal is not involutive, one obtains an $L_\infty$ algebra…
We study dynamical systems arising from word maps on simple groups. We develop a geometric method based on the classical trace map for investigating periodic points of such systems. These results lead to a new approach to the search of…
Let $F$ be an algebraically closed field of characteristic zero, and $G$ be a finite abelian group. If $A=\oplus_{g\in G} A_g$ is a $G$-graded algebra, we study degree-inverting involutions on $A$, i.e., involutions $*$ on $A$ satisfying…
This work is devoted to study the deformation of spacetime metrics as generalized conformal transformations. Some applications are also considered, in particular the equations of motion in deformed spacetime are studied.
Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
In this paper, we explain how generalized dynamical r-matrices can be obtained by (quasi-)Poisson reduction. New examples of Poisson structures and Poisson groupoid actions naturally appear in this setting. As an application, we use a…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
We consider a Lagrangian system on a fiber bundle and its gauge transformations depending on derivatives of dynamic variables and gauge parameters of arbitrary order. We say that gauge transformations form an algebra if they generate a…