Decoherence in quantum systems which are classically chaotic is studied. It is wellknown that a classically chaotic system when quantized loses many prominent chaotic traits. We show that interaction of the quantum system with an environment can under general circumstances quickly diminish quantum coherence and reenact some characteristic classical chaotic behavior. We use the Feynman-Vernon in...

An exact renormalization scheme is introduced for quantum Anosov maps (QAMs) on a torus for general boundary conditions (BCs), whose number is always finite. Given a QAM Û with k BCs and Planck’s constant h̄ = 2π/p (p integer), its nth renormalization iterate Û (n) = Rn(Û) is associated with k BCs for all n and with a Planck’s constant h̄ = h̄/kn. It is shown that the quasienergy eigenvalue proble...

We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessar...

We propose methods to construct high-quality pseudorandom number generators (RNG) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map, or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessary co...

Security of data is of prime importance. Security is a very complex and vast topic. One of the common ways to protect this digital data from unauthorized eavesdropping is encryption. This paper introduces an improved image encryption technique based on a chaotic 3D cat map and Turing machine in the form of dynamic random growth technique. The algorithm consists of two main sections: The first d...

After briefly recalling the concepts of recurrence and chaos in physics, the recurrence properties of arithmetic sets are examined following Gauss’ method, as exposed in part three of his Disquisitiones Arithmeticae. This problem in number theory is related to the physical problem of recurrence in deterministic chaos. Most possible forms of moduli are examined in detail with respect to their re...

‘Gradient grammar’ (Bresnan & Hay 2006) refers to statistical theories of language competence. A number of studies (Bod et al. 2003, Bresnan et al. 2005, Gries 2007, O’Connor et al. 2004, Snider & Zaenen 2006, Wasow & Arnold 2005, among others) have explored such probabilistic variation where speakers choose among grammatical options (dative and genitive alternations, complementizer optionality...

In systems with two degrees of freedom Arnold's theorem is used for studying non linear stability of the origin when the quadratic part of the Hamiltonian is a non definite form. In that case, a previous normalization of the higher orders is needed, which reduces the Hamiltonian to homogeneous polyno-mials in the actions. However, in the case of resonances it could not be possible to bring the ...

# I am most grateful to a number of individuals in South Africa, and especially to William Blankley, for supporting my fieldwork in that country and for providing comments. I must also express my deepest thanks to Robyn Arnold for a detailed editing of the manuscript and to Attila Havas for a number of comments on an earlier draft. But the usual disclaimer holds good. Finally, the views express...