Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-03-03Bitstream added on 2014-06-13T20:27:28Z : No. of bitstreams: 1 bronzi_ma_me_sjrp.pdf: 904425 bytes, checksum: 2344eb35a112034c2f1741b2e229f1ec (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Estudamos intersecções homoclínicas de variedades estável e instável de pontos peródicos. Toda intersecção homoclínica produz um comportamento curioso na dinâmiôa. Nosso modelo de tal fenômeno é a famosa ferradura de Smale, a qual é um conjunto hiperbólico para um difeomorfismo. Além disso, estudamos dinâmica não hiperbólica cuja perda de hiperbolicidade é divido à tangências homoclínicas. Elas tem um papel central na teoria de sistemas dinâmicos. O desdobramento de uma tangência homoclínica produz dinâmicas muito interessantes. Neste trabalho estudamos a criação de cascatas de bifurcações de duplicação de período e um esquema de renormalização para uma tangência homoclínica. / We study homoclinic intersection of stable and unstable manifolds of periodic points. Every homoclinic intersection produce a intricate behavior of the dynamics. Our model of such phenomena is the so called Smalesþs horseshoe, which is a hyperbolic set for a di eomorphism. We also study non hyperbolic dynamics whose lack of hyperbolicity is due to homoclinic tangencies. They play a central role in the theory of dynamical systems. The unfolding of a homoclinic tangency produce many interesting dynamics. In this work we study creation of cascade of period doubling bifurcations and a renormalization scheme for a homoclinic tangency.

Made available in DSpace on 2015-03-26T13:45:32Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1925307 bytes, checksum: 997942bc96f9ea8502e3844a314cbc0b (MD5) Previous issue date: 2010-04-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This dissertation is devoted to the study of wave planar fronts following the work developed by Aicardi in [Ai1]. She finds theses invariantsas a generalization of those introduced by Arnold for plane curves by using the Vassiliev Theory. In this work, we study and describe Aicardi's invariants as well as their properties. Moreover, by using the notions of bridges and chanel given in [MJ-RF] we obtain an alternative algorithm for the calculation os such invariants. / Esta dissertação é dedicada ao estudo dos invariantes de frentes de ondas planas seguindo o trabalho desenvolvido por F. Aicardi em [Ai1]. Ela encontra estes invariantes fazendo uma generalização dos invariantes de curvas planas introduzidos por Arnold utilizando a teoria de Vassiliev. Neste trabalho estudamos e descrevemos os invariantes de Aicardi, assim como suas propriedades. Além disso, utilizando as nações de pontes e canais de curvas dado em [MJ-RJ] apresentamos um algoritmo alternativo para o cálculo de tais invariantes.

Despite the fact that illiquid assets pose several difficulties regarding portfolio allocation problems for investors, more investors are increasing their allocation towards them. Alternative assets are characterized as being harder to value and trade because of their illiquidity which raises the question of how they should be managed from an allocation optimization perspective. In an attempt to demystify the illiquidity conundrum, shadow allocations are attached to the classical mean-variance framework to account for liquidity activities. The framework is further improved by replacing the variance for the coherent risk measure conditional value at risk (CVaR). This framework is then used to first stress test and optimize a theoretical portfolio and then analyze real-world data in a case study. The investors’ liquidity preferences are based on common institutional investors such as Foundations & Charities, Pension Funds, and Unions. The theoretical results support previous findings of the shadow allocations framework and decrease the allocation towards illiquid assets, while the results of the case study do not support the shadow allocations framework. / Trots det faktum att illikvida tillgångar medför flera svårigheter när det gäller portföljallokeringsproblem för investerare, så ökar allt fler investerare sin allokering mot dem. Alternativa tillgångar kännetecknas av att de är svårare att värdera och handla på grund av sin illikviditet, vilket väcker frågan om hur de ska hanteras ur ett allokeringsoptimeringsperspektiv. I ett försök att avmystifiera illikviditetsproblemet adderas skuggallokeringar till det klassiska ramverket för modern portföljteori för att ta hänsyn till likviditetsaktiviteter. Ramverket förbättras ytterligare genom att ersätta variansen mot det koherenta riskmåttet CVaR. Detta ramverk används sedan för att först stresstesta och optimera en teoretisk portfölj, och sedan analysera verkliga data i en fallstudie. Investerarnas likviditetspreferenser baseras på vanliga institutionella investerare såsom stiftelser & välgörenhetsorganisationer, pensionsfonder samt fackföreningar. De teoretiska resultaten stödjer tidigare forskning om ramverket för skuggallokeringer och sänker allokeringen mot illikvida tillgångar, samtidigt som resultaten från fallstudien inte stödjer ramverket för skuggallokeringar.