We introduce and study the classical and quantum mechanics of certain non hyperbolic maps on the unit square. These maps are modifications of the usual baker's map and their behaviour ranges from chaotic motion on the whole measure to chaos on a set of measure zero. Thus we have called these maps " lazy baker maps. " The aim of introducing these maps is to provide the simplest models of systems...

In this paper we introduce two innovative image and video watermarking algorithms. The paper’s main emphasis is on the use of chaotic maps to boost the algorithms’ security and resistance against attacks. By encrypting the watermark information in a one dimensional chaotic map, we make the extraction of watermark for potential attackers very hard. In another approach, we select embedding po...

Synchronization between chaotic systems has recently been a topic of great interest among physicists and engineers. In addition to theoretical results, a number of applications in communications and control have also been proposed. We have previously shown that identical chaotic maps can, under certain conditions, be synchronized by a common noise-like input. This raises the question whether th...

Haar wavelet is one of the best mathematical tools in image cryptography and analysis. Because of the specific structure, this wavelet has the ability which is combined with other mathematical tools such as chaotic maps. The rational order chaotic maps are one of clusters of chaotic maps which their deterministic behaviors have high sensitivity. In this paper, we propose a novel method of gradi...

This paper proposes a theorem to generate chaotic key stream from topologically conjugated maps of Tent Map. In this theorem, the condition for topological conjugation between Tent Map and a class of chaotic maps is first determined. Then, the chaotic attractor of the maps is divided into 2 unequal subintervals, the chaotic orbit is sampled once in n time iteration, and, finally, the independen...