Cantor exchange systems and renormalization

We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.

Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Uma perspectiva foucaudiana na auditoria à avaliação de desempenho na administração pública

Motivation: Auditing is not merely a collection of technical tasks but also a programmatic idea circulating in organizational environment, an idea which promises a certain style of control and organizational transparency (Power, 1998, p. 122) Performance appraisal within public organization aims to promote this organizational transparency and promote learning and improvement process both for employees and for the organization. However, we suggest that behind its clear intentions, there are some other goals tied to performance appraisal that could be seen as components of a discipline and surveillance systems to make the employee “knowable, calculable and administrative object” (Miller and Rose, 1990, p. 5). Objective: In Portuguese public organizations, performance appraisal follows the SIADAP (Performance Appraisal Systems for Public Administration). The objective of this study is to capture whatever employees of public organizations (appraisers and appraisee) perceived the performance appraisal system (SIADAP) as an appraisal model that promotes equity, learning and improvement or just as an instrument of control to which they feel dominated and watched over. Method: We developed an in-depth qualitative case study using semi-structured interviews with appraisers and their subordinates in the administrative department of a university institute of Medicine. The discourse of the participants was theoretically analyzed based on Foucauldian framework. Prior to qualitative data collection, we collected quantitative data, with a questionnaire, to measure the (un)satisfaction of employees with the all appraisal system. Findings: Although some key points of Foucault perspective were identified, its framework revealed some limitations to capture the all complexity of performance appraisal. Qualitative data revealed a significant tendency in discourses of appraisers and their subordinates considering SIADAP as an instrument that’s aims to introduced political rationalities and limits to the employer’s promotions within their careers. Contribution: This study brings a critical perspectives and new insights about performance appraisals in Portuguese’s public administrations. It is original contribution to management of human recourses in public administration and primary to audit of performance appraisal systems.