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...
متن کاملIteration of Differentiable Functions under m-Modal Maps with Aperiodic Kneading Sequences
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...
متن کاملReducing Quadratic Forms by Kneading Sequences
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...
متن کاملDynamics of continued fractions and kneading sequences of unimodal maps
In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the α-continued fraction transformations Tα and unimodal maps. This correspondence identifies bifurcation parameters in the two families, and allows one to transfer topological and metric properties from one setting to the other. As an application, we recover results ab...
متن کاملOn Aperiodic and Periodic Complementary Binary Sequences
We give direct and recursive constructions for aperiodic and periodic complementary sequences. Using these constructions, many missing entries in the table of Bömer and Antweiler [4] can be filled.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1989
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1989-0979221-0