Iterations of concave maps, the Perron-Frobenius theory and applications to circle packings
نویسندگان
چکیده
منابع مشابه
Ela Iterations of Concave Maps , the Perron – Frobenius Theory , and Applications to Circle Packings
The theory of pseudo circle packings is developed. It generalizes the theory of circle packings. It allows the realization of almost any graph embedding by a geometric structure of circles. The corresponding Thurston’s relaxation mapping is defined and is used to prove the existence and the rigidity of the pseudo circle packing. It is shown that iterates of this mapping, starting from an arbitr...
متن کاملIterations of concave maps, the Perron-Frobenius theory and applications to circle packings
The theory of pseudo circle packings is developed. It generalizes the theory of circle packings. It allows the realization of almost any graph embedding by a geometric structure of circles. The corresponding Thurston’s relaxation mapping is defined and is used to prove the existence and the rigidity of the pseudo circle packing. It is shown that iterates of this mapping, starting from an arbitr...
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By the use of Perron-Frobenius theory, simple proofs are given of the Fundamental Theorem of Demography and of a theorem of Cushing and Yicang on the net reproductive rate occurring in matrix models of population dynamics. The latter result, which is closely related to the Stein-Rosenberg theorem in numerical linear algebra, is further refined with some additional nonnegative matrix theory. Whe...
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This article provides sufficient conditions for positive maps on the Schatten classes Jp; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on J1, the space of trace class operators, to have a unique, stric...
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We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (In...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2002
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1087