The limit set of iterations of entire functions on wandering domains

We first establish any continuum without interiors can be a limit set of iterations of an entire function on an oscillating wandering domain, and hence arise as a component of Julia sets. Recently, Luka Boc Thaler showed that every bounded connected regular open set, whose closure has a connected complement, is an oscillating or an escaping wandering domain of some entire function. A natural question is: What kind of domains can be realized as a periodic domain of some entire function? In this paper, we construct a sequence of entire functions whose invariant Fatou components can be approached to a regular domain

N-[(Z)-3-(4-Chloro­benzo­yl)-1,3-thia­zolidin-2-yl­idene]cyanamide

The title compound, C11H8ClN3OS, was prepared by the reaction of N-cyano­imino­thia­zolidine, 2-amino­ethanethiol and triethyl­amine at 350 K. The dihedral angle between the two rings is 62.5 (8)°

catena-Poly[[[bis­[2,2′-(propane-1,3-diyl­dithio)bis­(1,3,4-thia­diazole)-κN 4]copper(II)]-bis­[μ-2,2′-(propane-1,3-diyldithio)bis­(1,3,4-thia­diazole)-κ2 N 4:N 4′]] bis­(perchlorate)]

In the title compound, {[Cu(C7H8N4S4)4](ClO4)2}n, the CuII atom, occupying a crystallographic inversion centre, is six-coordinated by six N atoms of three symmetry-related 2,2′-(propane-1,3-diyldithio)bis­(1,3,4-thia­diazole) (L) ligands in a slightly distorted octa­hedral geometry. The ligand L adopts two kinds of coordination modes in the crystal structure; one is a monodentate coordination mode and serves to complete the octa­hedral coordination of the Cu atom and the other is an N:N′-bidentate bridging mode in a trans configuration, bridging Cu atoms via translation symmetry along the b axis into a chain structure. The perchlorate ions serve as acceptors for inter­molecular C—H⋯O hydrogen bonds, which link the chains into a three-dimensional network

catena-Poly[[bis­(nitrato-κ2 O,O′)copper(II)]-μ-2,2′-(ethane-1,2-diyldithio)di-1,3,4-thia­diazole-κ2 N 4:N 4′]

In the title compound, [Cu(NO3)2(C6H6N4S4)]n, the CuII atom, occupying a crystallographic inversion centre, is six-coordinated by two N atoms of two 2,2′-[1,2-ethane­diyl­bis­(thio)]bis­[1,3,4-thia­diazole] ligands in trans positions, and four O atoms from two symmetry-related opposite nitrate anions, which are asymmetrically bonded, resulting in a strong distorted octa­hedral geometry of the central atom. The ethane group is equally disordered over two sites via another inversion centre. The bridging bidentate 2,2′-[1,2-ethanediylbis(thio)]bis­[1,3,4-thia­diazole] ligands link the CuII centres into a one-dimensional chain. The chains are inter­connected via inter­molecular S⋯O inter­actions [3.044 (4) and 3.084 (5) Å] and weak C—H⋯O hydrogen bonds, generating a three-dimensional supra­molecular structure

Poly[[tris­[μ-2,2′-(butane-1,4-diyl­dithio)bis­(1,3,4-thia­diazole)-κ2 N 4:N 4′]copper(II)] bis­(perchlorate)]

In the title compound, {[Cu(C8H10N4S4)3](ClO4)2}n, the CuII atom is located on a threefold inversion axis coordinated by six N atoms of symmetry-equivalent 2,2′-(butane-1,4-diyl­dithio)bis­(1,3,4-thia­diazole) ligands in a slightly distorted octa­hedral geometry. Adjacent CuII atoms are linked by the bridging bidentate thia­diazole ligands, which are situated about inversion centers. This leads to the formation of a three-dimensional network structure

Poly[[bis­(acetonitrile-κN)bis­[μ2-2,2′-(methyl­enedithio)bis­(1,3,4-thia­diazole)-κ2 N 4:N 4′]copper(II)] bis­(perchlorate) acetonitrile solvate]

In the title compound, {[Cu(C5H4N4S4)2(C2H3N)2](ClO4)2·C2H3N}n, the CuII atom occupies a crystallographic inversion centre and is six-coordinated by six N atoms of four symmetry-related 2,2′-(methyl­enedithio)bis­(1,3,4-thia­diazole) (L) ligands and two acetonitrile mol­ecules in a slightly distorted octa­hedral geometry. The ligand L adopts an N:N′-bidentate bridging mode in a trans configuration, bridging the Cu atoms via translation symmetry, forming a two-dimensional layer-like structure. The perchlorate ions serve as acceptors for inter­molecular C—H⋯O hydrogen bonds, which link the layers into a three-dimensional network. The ClO4 − anion is disordered with an occupation ratio of 0.658:0.342