A chaotic attractor may consist of some number of bands (disjoint connected subsets). In continuous maps multi-band chaotic attractors are cyclic, that means every generic trajectory visits the bands in the same order. We demonstrate that in discontinuous maps multi-band chaotic attractors may be acyclic. Additionally, a simple criterion is proposed which allows to distinguish easily between cy...

We consider discrete invertible dynamical systems L with the property that the kth iterate L k possesses (reversing) symmetries that are not possessed by L. A map U is called a (reversing) k-symmetry of L if k is the smallest positive integer for which U is a (reversing) symmetry of L k. In this paper we discuss the particular case that L possesses a cyclic reversing k-symmetry group. We derive...

When ƒ is single-valued we know that continuity is equivalent to the assertion that A, B closed imply f (A), f~(B) closed. When ƒ is multi-valued we take this as a definition of continuity. I t does not follow, as in the single-valued case, that f~~(B) is open if B is open. These definitions include both a single-valued map ( = continuous function) and its inverse. In this note we show that cer...

The Möbius-Kantor map {4 + 4, 3} [CMo, §8.8, 8.9] is a regular orientable map of type {8, 3} and genus 2. It is a 2-sheeted covering of the cube {4, 3}, branched over the centers of its six faces, each of which lifts to an octagonal face. Its (orientation-preserving) automorphism group is isomorphic to GL2(3), a double covering of the automorphism group PGL2(3) ∼= S4 of the cube. The aim of thi...

We investigate fixed points for p cyclic maps by introducing a new notion of p–cyclic infimum summing and generalized best proximity point maps. The idea generalizes some results about in order to widen the class sets which we can ensure existence uniqueness points. replacement classical notions distance between consecutive set arises from well-known group traveling salesman problem presents di...

The regular coverings of regular affine algebraic maps are considered, and a large family of totally ramified coverings—the so-called Steinberg and Accola coverings—are fully classified.

In this article we discuss relations between algebraic and dynamical properties of non-cyclic semigroups rational maps.

HODGE DECOMPOSITION AND MINIMAL MODELS FOR CYCLIC ALGEBRAS J. CHUANG AND A. LAZAREV Abstract. We show that an algebra over a cyclic operad supplied with an additional linear We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal m...

In a previous paper we have investigated subsumption in the presence of terminological cycles for the description logic EL, which allows conjunctions, existential restrictions, and the top concept, and have shown that the subsumption problem remains polynomial for all three types of semantics usually considered for cyclic definitions in description logics. In this paper we show that subsumption...