Nosso objetivo nesse trabalho é estudar o comportamento dos operadores de transferência em f0, 1gN2 , um associado ao deslocamento horizontal (se1 ) e outro associado ao deslocamento vertical (se2 ). Construímos uma equação cohomológica para fins de ampliar a gama de funções às quais os operadores de transferência se aplicam. Estudamos também o comportamento do operador de transferência obtido pela composição dos dois operadores citados e, em condições de comutatividade, encontramos um autovalor e uma autofunção associada, ambos estritamente positivos, e uma automedida para o operador dual, associada ao mesmo autovalor. Tal automedida é um estado de equilíbrio. Além disso, estudamos algumas propriedades ergódicas de transformações de blocos. / In this work we study the behavior of the transfer operators in f0, 1gN2 , one associated with horizontal shift (se1 ) and other associated with vertical shift (se2 ). We build a cohomological equation for the purpose of expanding the range of functions to which the transfer operators apply. We also study the behavior of the transfer operator obtained by the composition of the two cited operators and, in the conditions of commutativity, we find an eigenvalue and an associated eigenfunction, both strictly positive, and an eigen measuse for the dual operator, associated with the same eigenvalue. This eigen measure is an equilibrium state. Furthermore, we study some ergodic properties of block transformations.

Nosso objetivo nesse trabalho é estudar o comportamento dos operadores de transferência em f0, 1gN2 , um associado ao deslocamento horizontal (se1 ) e outro associado ao deslocamento vertical (se2 ). Construímos uma equação cohomológica para fins de ampliar a gama de funções às quais os operadores de transferência se aplicam. Estudamos também o comportamento do operador de transferência obtido pela composição dos dois operadores citados e, em condições de comutatividade, encontramos um autovalor e uma autofunção associada, ambos estritamente positivos, e uma automedida para o operador dual, associada ao mesmo autovalor. Tal automedida é um estado de equilíbrio. Além disso, estudamos algumas propriedades ergódicas de transformações de blocos. / In this work we study the behavior of the transfer operators in f0, 1gN2 , one associated with horizontal shift (se1 ) and other associated with vertical shift (se2 ). We build a cohomological equation for the purpose of expanding the range of functions to which the transfer operators apply. We also study the behavior of the transfer operator obtained by the composition of the two cited operators and, in the conditions of commutativity, we find an eigenvalue and an associated eigenfunction, both strictly positive, and an eigen measuse for the dual operator, associated with the same eigenvalue. This eigen measure is an equilibrium state. Furthermore, we study some ergodic properties of block transformations.

Nosso objetivo nesse trabalho é estudar o comportamento dos operadores de transferência em f0, 1gN2 , um associado ao deslocamento horizontal (se1 ) e outro associado ao deslocamento vertical (se2 ). Construímos uma equação cohomológica para fins de ampliar a gama de funções às quais os operadores de transferência se aplicam. Estudamos também o comportamento do operador de transferência obtido pela composição dos dois operadores citados e, em condições de comutatividade, encontramos um autovalor e uma autofunção associada, ambos estritamente positivos, e uma automedida para o operador dual, associada ao mesmo autovalor. Tal automedida é um estado de equilíbrio. Além disso, estudamos algumas propriedades ergódicas de transformações de blocos. / In this work we study the behavior of the transfer operators in f0, 1gN2 , one associated with horizontal shift (se1 ) and other associated with vertical shift (se2 ). We build a cohomological equation for the purpose of expanding the range of functions to which the transfer operators apply. We also study the behavior of the transfer operator obtained by the composition of the two cited operators and, in the conditions of commutativity, we find an eigenvalue and an associated eigenfunction, both strictly positive, and an eigen measuse for the dual operator, associated with the same eigenvalue. This eigen measure is an equilibrium state. Furthermore, we study some ergodic properties of block transformations.

Consider an iterated function system (IFS) that does not necessarily contract uniformly, but instead contracts on average after a finite number of iterations. Under some technical assumptions, previous work by Barnsley, Demko, Elton and Geronimo has shown that such an IFS has a unique invariant probability measure, whilst many (such as Peigné, Hennion and Hervé, Guivarc'h and le Page, Santos and Walkden) have shown that (for different function spaces) the transfer operator associated with the IFS is quasi-compact. A result due to Keller and Liverani allows one to deduce whether the transfer operator remains quasi-compact under suitable, small perturbations. The first part of this thesis proves a large deviations result for IFSs that contract on average using skew product transfer operators, a technique used by Broise to prove a similar result for dynamical systems. The remaining chapters introduce a notion of 'coupled IFSs', an analogue of the traditional coupled map lattices where the base, unperturbed behaviour is determined by an underlying dynamical system. We use transfer operators and Keller and Liverani's theorem to prove that quasi-compactness of the transfer operator is preserved for 'product IFSs' under small perturbations and for coupled IFSs. This allows us to prove a central limit theorem with a rate of convergence for the coupled IFS.

Zimbabwean migrants in South Africa often send financial support to their relatives in Zimbabwe. This financial support is known as remittances and is sent as cash or in-kind. This study investigated the characteristics of the South African-Zimbabwe remittance corridor. A critical investigation of the remittance channels used, the type of remittances sent, and the remittance transaction costs involved was done. Data for use in this study was collected through interviews with remittance service providers and by actual remittance transfers to Zimbabwe. A qualitative and quantitative analysis of data using statistical analysis techniques was done. From the analyzed data, it was observed that remittance service providers fall into two channels: formal and informal. The informal remittance channels were found to be the most popular in this corridor. The popularity of informal channels can be attributed to lower transaction costs and a lack of documentation needed from the sender. Informal remittance channels do not require the remittance sender to provide any identification document, therefore, undocumented Zimbabwean migrants opt for them. Long-distance buses that serve the South Africa-Zimbabwe route were found to be a popular channel of sending remittances - both cash and in-kind - to Zimbabwe. In-kind remittances have gained popularity due to the perennial lack of household consumer goods in Zimbabwe. Due to the national lockdown imposed in South Africa as a response to the Covid19 global pandemic, the study was unable to find the volume of remittances that is sent through the informal longdistance buses and trucks. The lockdown resulted in the closure of borders and non-essential travel was not permitted. The study found that the remittance transaction cost in the South AfricaZimbabwe corridor was higher than the global average cost of 6.84% (for formal channels) and the United Nations Sustainable Development Goal of 3% by the year 2030.

京都大学 / 0048 / 新制・課程博士 / 博士(人間・環境学) / 甲第19200号 / 人博第741号 / 新制||人||178(附属図書館) / 27||人博||741(吉田南総合図書館) / 32192 / 京都大学大学院人間・環境学研究科共生人間学専攻 / (主査)教授 宇敷 重廣, 教授 森本 芳則, 准教授 木坂 正史 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DGAM