Related papers: One Dimensional p-adic Integral Value Transformati…
We consider dynamical systems on the space of functions taking values in a free associative algebra. The system is said to be integrable if it possesses an infinite dimensional Lie algebra of commuting symmetries. In this paper we propose a…
A formalism of systematic construction of integrable non-autonomous deformations of soliton hierarchies is presented. The theory is formulated as an initial value problem (IVP) for an associated Frobenius integrability condition on a Lie…
We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the…
Connections between partial dynamcial systems, a generalized notion of partial dynamical systems defined by nested sequences of partial homeomorphisms, and triangular AF algebras which admit an integer-valued cocycle are established.
The search for new integrable (3+1)-dimensional partial differential systems is among the most important challenges in the modern integrability theory. It turns out that such a system can be associated to any pair of rational functions of…
Let $(X,d,f)$ be a topological dynamical system, where $(X,d)$ is a compact metric space and $f:X\to X$ is a continuous map. We define $n$-ordered empirical measure of $x\in X$ by \begin{align*}…
The concept of an intrinsic system can be extended to the case of collective octupole degrees of freedom by exploiting the symmetry properties with respect to transformations of the octahedral group O_h. Explicit formulas for scalar…
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the…
We study one-parameter expanding evolution families of simply connected domains in the complex plane described by infinite systems of evolution parameters. These evolution parameters in some cases admit Hamiltonian formulation and lead to…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…
In this paper we study the general concept of integrability in the broad sense within the frame of differential Galois theory. We concentrate on the gradient systems which are not integrable. In spite of it, if we consider them as the real…
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…
Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to visualise solutions in different ways. Using ubiquitous computing infrastructure, we…
We show that invertible transformations of dynamical variables can change the number of dynamical degrees of freedom. Moreover, even in cases when the number of dynamical degrees of freedom remains unchanged, the resulting dynamics can be…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely…
The details of second-order partial derivatives of rigid-body Inverse/Forward dynamics are provided. Several properties and identities using Spatial Vector Algebra are listed, along with their detailed derivations. The expressions build…