2024 Period of a discrete cat mapping

Period of a discrete cat mapping

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August undefined, 2024

WebChaotic dynamics is an important source for generating pseudorandom binary sequences (PRBS). Much efforts have been devoted to obtaining period distribution of the generalized discrete Arnold's Cat map in various domains using all kinds of theoretical methods, including Hensel's lifting approach. WebOct 1, 2012 · The period distribution results help in the design and analysis of various systems when a given period is of crucial importance. However, the exact detailed period …

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WebApr 23, 2014 · Period of a discrete cat mapping. Amer. Math. Monthly 99 (7) ... Informal remarks on the orbit structure of discrete approximations to chaotic maps. Experiment. Math. 7 (4) (1998), 317 ... Long periodic orbits of the triangle map. Proc. Amer. Math. Soc. 97 (2) (1986), 247 ... WebNov 13, 2011 · The defining characteristic of this map is that it has the property that when the NxN grid is a picture whose pixels are assigned (x,y) coordinates, the map scrambles … highfield learning academy blackpool

The Graph Structure of the Generalized Discrete Arnold

WebChaotic dynamics is an important source for generating pseudorandom binary sequences (PRBS). Much efforts have been devoted to obtaining period distribution of the … WebWe may formulate the following deﬁnition because the discrete-time dynamical system, i.e., the set of rules imposed by Arnold’s cat map, will follow the Poincaré Recurrence Theorem and hence be periodic. Deﬁnition 1. The minimal period of Arnold’s discrete cat map is the smallest positive integer n such that A n 1 0 0 1 (mod N). WebA discrete dynamical system known as Arnold’s Discrete Cat Map (Arnold’s DCM) is given by (xt+1,yt+1) = (xt +yt,xt +2yt) mod N, ... So a 3×3 image has period M = 4 since four iterations of the cat map were needed to return the image to its original state. 2. pixel dimension of image (N ×N) iterations to restore image (period) how hot can a crock pot get

Period Distribution of the Generalized Discrete Arnold Cat Map for ...

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WebThe discrete cat map From order to chaos and back. Sample mapping on a picture of 150x150 pixels. The numbers shows the iteration step. After 300 iterations arriving at the original image Sample mapping on a picture of a pair of cherries. WebNov 13, 2011 · Periods of the discretized Arnold Cat Map and its extension to n dimensions Joe Nance A discrete dynamical system known as Arnold's Discrete Cat Map (Arnold's … highfield learning loginWebJun 27, 2014 · Fig. 1: Lena image(512x51 2) with Arnold’s cat map applied. Period of the image is 384. The result of the map applied k . ... Period of a Discrete Cat Mapping. Article. Aug 1992; Freeman J ... how hot can a gtx 1070 get

"WebThe discrete map is a subsequent development of the origional idea. The original cat map on the torus should come first, and only after that we can introduce the further developments.-- Pokipsy76 09:55, 10 July 2006 (UTC) [ reply] I think that is beside the point. The current formulation applies to continuous and discrete domains. " - Period of a discrete cat mapping

Period of a discrete cat mapping

WebJan 5, 2012 · Period Distribution of Generalized Discrete Arnold Cat Map for [Math Processing Error] Abstract: In this paper, we analyze the period distribution of the … WebDec 21, 2024 · Chaotic dynamics is an important source for generating pseudorandom binary sequences (PRNS). Much efforts have been devoted to obtaining period distribution of the generalized discrete Arnold's Cat map in various domains using all kinds of theoretical methods, including Hensel's lifting approach. Diagonalizing the transform …

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WebThe Arnold Cat Map is a discrete system that stretches and folds its trajectories in phase space. 2. Arnold cat map has a unique hyperbolic fixed point ... For example, a 101 x 101 image has a period of twenty-five; whereas, a 124 x 124 image, as we just learned, has a period of fifteen. Other luminaries have found a relationship where WebJan 13, 2024 · Much efforts have been devoted to obtaining period distribution of the generalized discrete Arnold's Cat map in various domains using all kinds of theoretical methods, including Hensel's lifting approach. Diagonalizing the transform matrix of the map, this article gives the explicit formulation of any iteration of the generalized Cat map.

WebFor a given N the period mN of the mapping (1.6) is the smallest positive integer n such that u2= -0 (mod N) and (1.8) U2n_-1 1 (mod N)-. [Note that (1.8) implies U2n+1 U2n+2 1 (mod N).] Thus, the period is related to the divisibility properties of Fibonacci numbers. 604 … WebIn the paper, for the discrete Arnold cat map, the minimal period formulae are obtained for a compos-ite N, and the period formulae are given for a prime N, while an algorithm is …

WebPeriod of a Discrete Cat Mapping Freeman J. Dyson and Harold Falk 1. INTRODUCTION. In studying the dynamics of a mechanical system one uses time averages and phase-space … WebJun 15, 1994 · The generalized discrete Arnold cat map is adopted in various cryptographic and steganographic applications where chaos is employed. In this paper, we analyze the period distribution of this map. A systematic approach for addressing the general period distribution problem for any integer value of the modulus N is outlined, followed by a ...

WebOct 1, 2012 · It is easy to find that the map must have a period, i.e. for a given initial value x ( 0) = [ x ( 0), y ( 0)] T, after some iterations the map returns to its original value x ( 0). This phenomena possesses both theoretical interests and application significance.

WebDec 1, 2024 · Period distribution of the generalized discrete arnold cat map for n = 2 e IEEE Trans. Inf. Theory , 59 ( 5 ) ( 2013 ) , pp. 3249 - 3255 View in Scopus Google Scholar highfield leadership academy vacanciesWebAug 1, 2012 · The paper first studies the period of the discrete Arnold cat map. When the modulo is composite, the formulae are developed to calculate the minimal period. When … highfield learning food log inWebAug 1, 2012 · The paper first studies the period of the discrete Arnold cat map. When the modulo is composite, the formulae are developed to calculate the minimal period. When the modulo is prime, the formulae calculating the period are given and an algorithm is proposed in order to determine the minimal period. how hot can a graphics card getWebPeriod Distribution of the Generalized Discrete Arnold Cat Map for Abstract: The Arnold cat map is employed in various applications where chaos is utilized, especially chaos-based cryptography and watermarking. In this paper, we study the problem of period distribution of the generalized discrete Arnold cat map over the Galois ring \BBZ 2 e . how hot can a gas stove getWebJun 25, 2024 · In this regard, a Russian mathematician Vladimir Igorevich Arnold proposed a new two dimensional map based on continuous automorphism on the torus (CAT) in 1960’s. A complete chaotic system can be constructed by utilizing Arnold cat transformation. how hot can a gpu runWebOct 1, 2005 · Two interesting conjectures on the period of Arnold transformation are given. When making digital images scrambling by Arnold transformation, it is important to know the period of the transformation for the image. ... Dyson F J, Falk H. Period of a discrete cat mapping [J]. The Amer Math Monthly, 1992, 99: 603–614. Article MathSciNet Google ... how hot can a heat pump getWebJan 31, 2024 · December 1971 · Discrete Mathematics Amos Altshuler Given a map M on a 2-manifold of genus ⩾1, it is generally not known when is the map geometrically embeddable in R3. Sufficient conditions... how hot can a flamethrower burn