Related papers: Integral Value Transformations: A Class of Discret…
A notion of dimension preservative map, \textit{Integral Value Transformations} (IVTs) is defined over $\mathbb{N}^k$ using the set of $p$-adic functions. Thereafter, two dimensional \textit{Integral Value Transformations} (IVTs) is…
In this paper, a set of transformations T^(p,k) is defined on N_0^K to N_0. Some basic and na\"ive mathematical structure of T^(p,1) are adumbrated and introduced the concept of discrete dynamical systems through IVTs. Latterly, some…
In this paper, the notion of Integral Value Transformations (IVTs), a class of Discrete Dynamical Maps has been introduced. Then notion of Affine Discrete Dynamical System (ADDS) in the light of IVTs is defined and some rudimentary…
Integral Value Transformation (IVT) is a family of transformations from N0kto N0. An algebraic result has been established in p-adic IVT systems and an application of the result is described in this paper. The result in this paper provides…
An interval translation map (ITM) is a piece-wise translation $T \colon I \to I$ defined on a finite partition $I_1, \ldots, I_r$ of an interval $I$ into $r \ge 2$ subintervals. In contrast to classical interval exchange transformations…
An interval translation map (ITM) is a map $T \colon I \to I$ defined as a piecewise translation on a finite partition of an interval $I$ into $r \ge 2$ subintervals. Unlike classical interval exchange transformations (IETs), the images of…
Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…
We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the…
Interval translation maps (ITMs) are a non-invertible generalization of interval exchange transformations (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. In…
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…
It is shown that each integrable mapping is connected with a hierarchical completely integrable sytem of equations of evolution type which are invariant with respect to the transformation described by this mapping.
We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not…
We consider continuous, translation-commuting transformations of compact, translation-invariant families of mappingsfrom finitely generated groups into finite alphabets. It is well-known that such transformations and spaces can be described…
Deep neural networks are applied in more and more areas of everyday life. However, they still lack essential abilities, such as robustly dealing with spatially transformed input signals. Approaches to mitigate this severe robustness issue…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
An interval translation map (ITM) is a piece-wise translation $T \colon I \to I$ defined on a finite partition $I_1, \ldots, I_r$ of an interval $I$ into $r \ge 2$ subintervals. In contrast to classical interval exchange transformations…
We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including…
Carry Value Transformation (CVT) is a model of discrete dynamical system which is one special case of Integral Value Transformations (IVTs). Earlier in [5] it has been proved that sum of two non-negative integers is equal to the sum of…
Transferability estimation identifies the best pre-trained models for downstream tasks without incurring the high computational cost of full fine-tuning. This capability facilitates deployment and advances the pre-training and fine-tuning…
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form,…