Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

On the KAM - Theory Conditions for the Kirchhoff Top

* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.

Criação de valor para o cliente: um estudo exploratório sobre programas de Key Account Management (KAM)

Nas últimas décadas, a maturidade de alguns mercados, a globalização e o crescente poder de barganha dos clientes aumentam ainda mais a necessidade das empresas em manterem e desenvolverem de forma eficaz seus clientes mais importantes. Neste contexto, ganham relevância os programas de Key Account Management (KAM), iniciativas corporativas que tratam de forma especial os clientes mais importantes do fornecedor. Para obter o desempenho financeiro superior, o programa de KAM precisa criar valor para o cliente para posterior apropriação de valor pelo fornecedor. Contudo, a maioria dos estudos enfatiza a apropriação de valor pelo fornecedor, porém poucas pesquisas investigam a criação de valor para o cliente em programas de KAM. Além disso, a maioria das pesquisas em marketing de relacionamento ainda foca muito nos impactos positivos do relacionamento. Dessa forma, é importante analisar empiricamente como é a implementação da criação de valor para o cliente em programas de KAM, identificando as principais dimensões e os fatores críticos. O objetivo do presente estudo é analisar o processo de criação de valor para o cliente em programas de Key Account Management (KAM) e propor um modelo de criação de valor para o cliente segundo a perspectiva da empresa fornecedora. As análises e o modelo são elaborados a partir de um processo de investigação abdutiva, ou seja, a combinação entre a fundamentação teórica sobre o conceito de valor e programas de KAM e a análise de conteúdo de 22 entrevistas em profundidade com especialistas em programas de KAM, profissionais de marketing/vendas que trabalham por pelo menos cinco anos com programas de KAM em grandes empresas no Brasil. O modelo proposto explica de forma integrada e sistemática como é a criação de valor para o cliente em programas de KAM segundo cinco dimensões (Desenvolvimento de relacionamentos; Entendimento dos direcionadores de valor; Desenvolvimento da proposta de valor; Comunicação da proposta de valor; e mensuração de valor), quatro moderadores (Orientação relacional do cliente; Formalização do programa de KAM para o cliente; Abordagem do fornecedor: \"orientada ao cliente\" vs. \"orientar o cliente\"; e Fit estratégico entre o fornecedor e o cliente) e três riscos (Não entrega do valor básico para o cliente; Rotatividade do Key Account Manager; e Sentimento de injustiça do cliente). Contribui-se com a teoria sobre o tema, ao incluir uma dimensão específica no modelo para desenvolvimento de relacionamentos do nível da díade (organização-organização) e indivíduo (funcionário-funcionário), e ao abordar não somente aspectos positivos do relacionamento, mas também os aspectos negativos (ou riscos da criação de valor para o cliente). Contribui-se também para a prática, ao prover uma visão mais ampla, sistemática e integradora dos diversos elementos da criação de valor para o cliente aos executivos das empresas que possuem programas de KAM, e ao recomendar práticas organizacionais que servem como guias para a tomada de decisão dos gestores de programas de KAM. Ademais, como a parte empírica do estudo é baseada no contexto brasileiro, amplia-se o conhecimento sobre KAM no Brasil. Por fim, apresentam-se as limitações do estudo com a agenda de pesquisas futuras

Ghosts of order on the frontier of chaos

What kinds of motion can occur in classical mechanics? We address this question by looking at the structures traced out by trajectories in phase space; the most orderly, completely integrable systems are characterized by phase trajectories confined to low-dimensional, invariant tori. The KAM theory examines what happens to the tori when an integrable system is subjected to a small perturbation and finds that, for small enough perturbations, most of them survive.

The KAM theory is mute about the disrupted tori, but, for two-dimensional systems, Aubry and Mather discovered an astonishing picture: the broken tori are replaced by "cantori," tattered, Cantor-set remnants of the original invariant curves. We seek to extend Aubry and Mather's picture to higher dimensional systems and report two kinds of studies; both concern perturbations of a completely integrable, four-dimensional symplectic map. In the first study we compute some numerical approximations to Birkhoff periodic orbits; sequences of such orbits should approximate any higher dimensional analogs of the cantori. In the second study we prove converse KAM theorems; that is, we use a combination of analytic arguments and rigorous, machine-assisted computations to find perturbations so large that no KAM tori survive. We are able to show that the last few of our Birkhoff orbits exist in a regime where there are no tori.

Über die Existenz invarianter Tori in Hamiltonschen Systemen, die bis auf eine endlich oft differenzierbare Störung analytisch und integrabel sind

Es wird die Existenz invarianter Tori in Hamiltonschen Systemen bewiesen, die bis auf eine 2n-mal stetig differenzierbare Störung analytisch und integrabel sind, wobei n die Anzahl der Freiheitsgrade bezeichnet. Dabei wird vorausgesetzt, dass die Stetigkeitsmodule der 2n-ten partiellen Ableitungen der Störung einer Endlichkeitsbedingung (Integralbedingung) genügen, welche die Hölderbedingung verallgemeinert. Bisher konnte die Existenz invarianter Tori nur unter der Voraussetzung bewiesen werden, dass die 2n-ten Ableitungen der Störung hölderstetig sind.

Perturbations of Systems Describing the Motion of a Particle in Central Fields

The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.

Using extreme value theory to measure value-at-risk for daily electricity spot prices

The recent deregulation in electricity markets worldwide has heightened the importance of risk management in energy markets. Assessing Value-at-Risk (VaR) in electricity markets is arguably more difficult than in traditional financial markets because the distinctive features of the former result in a highly unusual distribution of returns-electricity returns are highly volatile, display seasonalities in both their mean and volatility, exhibit leverage effects and clustering in volatility, and feature extreme levels of skewness and kurtosis. With electricity applications in mind, this paper proposes a model that accommodates autoregression and weekly seasonals in both the conditional mean and conditional volatility of returns, as well as leverage effects via an EGARCH specification. In addition, extreme value theory (EVT) is adopted to explicitly model the tails of the return distribution. Compared to a number of other parametric models and simple historical simulation based approaches, the proposed EVT-based model performs well in forecasting out-of-sample VaR. In addition, statistical tests show that the proposed model provides appropriate interval coverage in both unconditional and, more importantly, conditional contexts. Overall, the results are encouraging in suggesting that the proposed EVT-based model is a useful technique in forecasting VaR in electricity markets. (c) 2005 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

Feminist Disability Theory: Domestic Violence Against Women with a Disability

Women with a disability continue to experience social oppression and domestic violence as a consequence of gender and disability dimensions. Current explanations of domestic violence and disability inadequately explain several features that lead women who have a disability to experience violent situations. This article incorporates both disability and material feminist theory as an alternative explanation to the dominant approaches (psychological and sociological traditions) of conceptualising domestic violence. This paper is informed by a study which was concerned with examining the nature and perceptions of violence against women with a physical impairment. The emerging analytical framework integrating material feminist interpretations and disability theory provided a basis for exploring gender and disability dimensions. Insight was also provided by the women who identified as having a disability in the study and who explained domestic violence in terms of a gendered and disabling experience. The article argues that material feminist interpretations and disability theory, with their emphasis on gender relations, disablism and poverty, should be used as an alternative tool for exploring the nature and consequences of violence against women with a disability.