Kneading sequences for double standard maps
نویسندگان
چکیده
منابع مشابه
Complexity of unimodal maps with aperiodic kneading sequences
It is well established that a formal language generated from a unimodal map is regular if and only if the map’s kneading sequence is either periodic or eventually periodic. A previously proposed conjecture said that if a language generated from a unimodal map is context-free, then it must be regular, i.e. there exists no proper context-free language which can be generated from a unimodal map. T...
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Abstract. The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. We also define a Markov partition by rectangles for the phase space of these maps. A direct consequence of these results is the rigorous computati...
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We introduce an invertible operation on finite sequences of positive integers and call it “kneading”. Kneading preserves three invariants of sequences — the parity of the length, the sum of the entries, and one we call the “alternant”. We provide a bijection between the set of sequences with alternant a and parity s and the set of Zagier-reduced indefinite binary quadratic forms with discrimina...
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We consider the dynamical system A, T , whereA is a class of differentiable functions defined on some interval and T :A → A is the operator Tφ : f ◦φ, where f is a differentiablem-modal map. Using an algorithm, we obtained some numerical and symbolic results related to the frequencies of occurrence of critical values of the iterated functions when the kneading sequences of f are aperiodic. More...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2009
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm206-0-5