Chaotic Unimodal and Bimodal Maps
نویسنده
چکیده
We describe up to conjugacy all unimodal and bimodal maps that are chaotic, by giving necessary and sufficient conditions for unimodal and bimodal maps of slopes ±s to be transitive.
منابع مشابه
On the inadequacy of unimodal maps for cryptographic applications
The security of chaos-based cryptosystems is closely related to the possibility of recovering control parameters and/or initial conditions from partial information on the associated chaotic orbits. In this paper we analyze this possibility for the case of unimodal maps. We show a meaningful set of contexts where the dynamics of unimodal maps can be reconstructed, which means a relevant reductio...
متن کاملOn a New Bimodal Normal Family
The unimodal distributions are frequently used in the theorical statistical studies. But in applied statistics, there are many situations in which the unimodal distributions can not be fitted to the data. For example, the distribution of the data outside the control zone in quality control or outlier observations in linear models and time series may require to be a bimodal. These situations, oc...
متن کاملA Proof That S-unimodal Maps Are Collet-eckmann Maps in a Specific Range of Their Bifurcation Parameters
Generally, Collet-Eckmann maps require unimodality and multimodality. The inverse is not true. In this paper, we will prove that S-unimodal maps are Collet-Eckmann maps in a specific range of their bifurcation parameters. The proof is based on the fact that the family of robustly chaotic unimodal maps known in the literature are all topologically conjugate to one another and the fact that if tw...
متن کامل4 Irreducible complexity of iterated symmetric bimodal maps
We introduce a tree structure for the iterates of symmetric bi-modal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a *-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the *-product induced on the associated Markov shifts.
متن کاملRobust Chaos in Polynomial unimodal Maps
Robust chaos occurs when a dynamical system has a neighborhood in parameter space such that there is one unique chaotic attractor, and no periodic attractors are present [Barreto et al., 1997; Banerjee et al., 19981. This behavior, expected to be relevant for any practical applications of chaos, was shown to exist in a general family of piecewise-smooth twodimensional maps, but conjectured to b...
متن کامل