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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Subordinação fractal para operadores de Schrödinger unidimensionais

Bazão, Vanderléa Rodrigues 16 February 2016 (has links)
Submitted by Livia Mello (liviacmello@yahoo.com.br) on 2016-09-21T17:48:16Z No. of bitstreams: 1 TeseVRB.pdf: 1791186 bytes, checksum: 970f4dd11b38f69a19ad04406ec5f723 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:47:56Z (GMT) No. of bitstreams: 1 TeseVRB.pdf: 1791186 bytes, checksum: 970f4dd11b38f69a19ad04406ec5f723 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:48:02Z (GMT) No. of bitstreams: 1 TeseVRB.pdf: 1791186 bytes, checksum: 970f4dd11b38f69a19ad04406ec5f723 (MD5) / Made available in DSpace on 2016-10-10T14:48:08Z (GMT). No. of bitstreams: 1 TeseVRB.pdf: 1791186 bytes, checksum: 970f4dd11b38f69a19ad04406ec5f723 (MD5) Previous issue date: 2016-02-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / We study fractal subordinacy theory for one-dimensional Schrödinger operators. First, we review results on Hausdorff subordinacy for discrete one-dimensional Schrödinger operators in order to analyze the differences and similarities of these results with respect to the packing setting. By using methods of packing subordinacy, we have obtained pac- king continuity properties of spectral measures of such operators. Then, we apply these methods to Sturmian operators with rotation number of quasibounded density to show that they have purely α-packing continuous spectrum. Moreover, we show that spectral fractal dimensional properties of discrete Schrödinger operators with Sturmian potentials of bounded density and with sparse potentials are preserved under suitable polynomial decaying perturbations, when the spectrum of these perturbed operators have some singular continuous component. Finally, we performed an introductory study of fractal subordinacy for continuous one-dimensional Schrödinger operators defined in bounded intervals. / Estudamos as chamadas teorias de subordinação fractal para operadores de Schrödinger unidimensionais. Primeiramente, realizamos um levantamento dos resultados sobre subordinação de Hausdorff para operadores de Schrödinger unidimensionais discretos a fim de analisar as diferenças e semelhanças destes resultados com respeito à medida de empacotamento. Usando-se métodos de subordinação de empacotamento, obtivemos propriedades de continuidade das medidas espectrais de tais operadores com respeito a medidas de empacotamento. Então, aplicamos tais métodos na verificação de que operadores sturmianos com número de rotação de densidade quase limitada possuem espectro puramente α-empacotamento contínuo. Ademais, verificamos que propriedades dimensionais fractais de operadores de Schrodinger discretos, gerados por potenciais sturmianos de densidade limitada e por uma classe de potenciais esparsos, são preservadas sob perturbações adequadas com decaimento polinomial, quando o espectro destes operadores perturbados possuir alguma componente singular contínua. Por fim, realizamos um estudo introdutório sobre subordinação fractal para operadores de Schrödinger unidimensionais contínuos definidos em intervalos limitados.

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