The spectral problem, substitutions and iterated monodromy
نویسندگان
چکیده
We provide a self-similar measure for the self-similar group G acting faithfully on the binary rooted tree, defined as the iterated monodromy group of the quadratic polynomial z + i. We also provide an Lpresentation for G and calculations related to the spectrum of the Markov operator on the Schreier graph of the action of G on the orbit of a point on the boundary of the binary rooted tree.
منابع مشابه
Monodromy problem for the degenerate critical points
For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...
متن کاملController Placement in Software Defined Network using Iterated Local Search
Software defined network is a new computer network architecture who separates controller and data layer in network devices such as switches and routers. By the emerge of software defined networks, a class of location problems, called controller placement problem, has attracted much more research attention. The task in the problem is to simultaneously find optimal number and location of controll...
متن کاملHyperbolic spaces from self-similar group actions
Self-similar group actions (or self-similar groups) have proved to be interesting mathematical objects from the point of view of group theory and from the point of view of many other fields of mathematics (operator algebras, holomorphic dynamics, automata theory, etc). See the works [BGN02, GNS00, Gri00, Sid98, BG00, Nek02a], where different aspects of self-similar groups are studied. An import...
متن کاملIterated Local Search Algorithm for the Constrained Two-Dimensional Non-Guillotine Cutting Problem
An Iterated Local Search method for the constrained two-dimensional non-guillotine cutting problem is presented. This problem consists in cutting pieces from a large stock rectangle to maximize the total value of pieces cut. In this problem, we take into account restrictions on the number of pieces of each size required to be cut. It can be classified as 2D-SLOPP (two dimensional single large o...
متن کاملBlocks of monodromy groups in complex dynamics
Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real grap...
متن کامل