arXiv subjects

R. Lozi

Publications and source records attributed to R. Lozi.

3 recordsLinked to original sources

arXiv2009

Global Orbit Patterns for Dynamical Systems On Finite Sets

In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set $X$ allows us to describe precisely the behaviour of such systems. We can predict by means of closed formulas, the number of gop of the set of all the function from $X$ to itself. We also explore, using the brute force of computers, some subsets of locally rigid functions on $X$, for which interesting patterns of periodic orbits are found.

math.DS↗

arXiv2008

New Enhanced Chaotic Number Generators

We introduce new families of enhanced chaotic number generators in order to compute very fast long series of pseudorandom numbers. The key feature of these generators being the use of chaotic numbers themselves for sampling chaotic subsequence of chaotic numbers in order to hide the generating function. We explore numerically the properties of these new families and underline their very high qualities and usefulness as CPRNG when series are computed up to 10 trillions iterations.

math.DS↗

arXiv2007

Giga-Periodic Orbits for Weakly Coupled Tent and Logistic Discretized Maps

We introduce new models of very weakly coupled logistic and tent maps for which orbits of very long period are found. The length of these periods is far greater than one billion. The property of these models relatively to the distribution of the iterated points (invariant measure) is described.

math.DS↗