Let (I, T ) be the inverse limit space of a post-critically finite tent map. Conditions are given under which these inverse limit spaces are pairwise nonhomeomorphic. This extends results of Barge & Diamond [2].

In this paper, statistical analysis of watermarking schemes based on correlation detection is presented. Statistical properties of watermark sequences generated by piecewise-linear Markov maps are exploited, resulting in superior watermark detection reliability. Correlation/spectral properties of such sequences are easily controllable, a fact that affects the watermarking system performance. A ...

It is well known that the average position or barycenter of generic orbits for the standard tent map is 0.5. Periodic orbits are exceptional orbits in the sense that most of them have barycenters different from 0.5. In this paper we prove that for any positive integer n, there exist n distinct periodic orbits for the standard tent map with the same barycenter. We also provide some patterns of p...

In their celebrated ”Period three implies chaos” paper, Li and Yorke proved that if a continuous interval map f has a period 3 point then there is an uncountable scrambled set S on which f has very complicated dynamics. One question arises naturally: Can this set S be chosen invariant under f? The answer is positive for turbulent maps and negative otherwise. In this note, we shall use symbolic ...

It is shown that every unimodal map is realized as a restriction of a simple map defined on the unit disc to a part of its boundary. Our two-dimensional map is called a full-folding map, which is defined generally on a compact metric space. It is a generalization of the full tent map in that it has two homeomorphic inverse maps and thus every non-critical point has two inverse images.

Corresponding Author: Muhammad Asif Khan Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Darul Ridzuan, 31750 Perak, Malaysia Email: [email protected] Abstract: Robust chaotic maps with wide robust region are favored in cryptography as it extends the key length. Chaotic tent map has robust chaos for control parameter μ = 2. Perturbation of control parameter v...

The intriguing characteristics of chaotic maps have prompted researchers to use these sequences in watermarking systems to good effect. In this paper we aim to use a tent map to encrypt the binary logo to achieve a like-noise signal. This approach makes extraction of the watermark signal by potential attacker very hard. Embedding locations are selected based on certain principles. Experimental ...