2015/11/13 by Puneet Kumar Patra, Patra, Puneet Kumar
Economics, Econometrics and Finance · Physics and Astronomy · Mathematics · #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1511.04236
A new discrete time-reversible map of a unit square onto itself is proposed.\nThe map comprises of piecewise linear two-dimensional operations, and is able\nto represent the macroscopic features of both equilibrium and nonequilibrium\ndynamical systems. Our operations are analogous to sinusoidally driven shear in\nthe two dimensions, and a radial compression/expansion of a point lying\noutside/inside a circle centered around origin. Depending upon the radius, the\nmap transitions from being ergodic and nondissipative (like in equilibrium\nsituations) to a limit cycle through intermediate multifractal situations (like\nin nonequilibrium situations). All dissipative cases of the proposed map\nsuggest that the Kaplan -- Yorke dimension is smaller than the embedding\ndimension, a feature typically arising in nonequilibrium steady-states. The\nproposed map differs from the existing maps like the Baker's map and Arnold's\ncat map in the sense that (i) it is reversible, and (ii) it generates an\nintricate multifractal phase-space portrait.\n