DSpace Coleção: PAPGM

Sombreamento e estabilidade estrutural forte em Dinâmica Linear

Tue, 29 Jul 2025 00:00:00 GMT

Título: Sombreamento e estabilidade estrutural forte em Dinâmica Linear Autor(es): Azevedo, Mateus Vinicius Santos de Orientador: Costa Júnior, Fernando Vieira Abstract: In this work, we present the class of hyperbolic operators and their connection with the well-established concepts of shadowing and strong structural stability in discrete dynamical systems and ergodic theory. We then examine a characterization of weighted shift operators on c0 or ℓp spaces (where 1 ≤ p < ∞) satisfying the shadowing property, as demonstrated by N. C. Bernardes Jr. and A. Messaoudi (2020). Furthermore, we analyze how F. Bayart (2021) established that, in this framework, the shadowing property is equivalent to strong structural stability. Editor: Universidade Federal da Paraíba Tipo: Dissertação

Nested Hilbert schemes on Hirzebruch surfaces and quiver varieties

Tue, 20 Feb 2024 00:00:00 GMT

Título: Nested Hilbert schemes on Hirzebruch surfaces and quiver varieties Autor(es): Santos, Pedro Henrique dos Orientador: Bruzzo, Ugo Abstract: Hilbert schemes were introduced by Grothendieck. They are a fundamental example of the notion of moduli spaces of geometric structures. The work of Nakajima on the properties of the Hilbert schemes of points of the complex plane has been the basis of many works that try to understand the properties of Hilbert schemes of other 2- dimensional varieties and also for higher dimensions. Furthermore, the nested Hilbert scheme of points on the complex plane was studied by von Flach, Jardim and Lanza. Moreover, Bartocci, Bruzzo, Lanza and Rava obtained a quiver description to the Hilbert scheme of points of the total space Ξn of appropriate line bundles over the projective line. In this work we show that the nested Hilbert scheme of points on the last varieties, parameterizing pairs of nested 0-cycles, is the quiver variety associated with a suitable quiver with relations, generalizing previous work about nested Hilbert schemes on the complex plane, in one direction, and about the Hilbert schemes of points of Ξn in another direction. Editor: Universidade Federal da Paraíba Tipo: Tese

Strongly indefinite problems with exponential growth in the plane

Thu, 29 Feb 2024 00:00:00 GMT

Título: Strongly indefinite problems with exponential growth in the plane Autor(es): Menezes, Marta Nascimento Orientador: Severo, Uberlandio Batista Abstract: In this work, we study questions related to the existence of ground state and nontrivial solution for some classes of strongly inde nite problems with exponential growth in the plane. Firstly, we study Hamiltonian systems, which have been widely addressed in the last years in the mathematical study of standing wave solutions in nonlinear optics. Secondly, we deal with a class of periodic Schrödinger equations involving exponential critical growth, in which we do not use the classic Ambrosetti-Rabinowitz condition. In order to obtain our results, we use variational methods, namely, a reduction method and linking theorems. Editor: Universidade Federal da Paraíba Tipo: Tese

Mean Curvature Flow Solitons in a GRW Spacetime and CMC Free Boundary Hypersurfaces in Rotational Domains

Tue, 30 Jul 2024 00:00:00 GMT

Título: Mean Curvature Flow Solitons in a GRW Spacetime and CMC Free Boundary Hypersurfaces in Rotational Domains Autor(es): Sindeaux, Joyce Saraiva Orientador: Freitas, Allan George de Carvalho Abstract: In this work, we study two themes. First, we study a n-dimensional spacelike mean curvature flow solitons related to the closed conformal timelike vector field K = f(t)∂t (t ∈ I ⊂ R) which is globally defined on an generalized Robertson-Walker (GRW) spacetime −I×fMn+p with warping function f ∈ C∞(I) and Riemannian fiber Mn+p, these are particular cases of trapped submanifolds, and we obtain rigidity and non-existence results for this submanifold class via applications of suitable generalized maximum principles and under certain constraints on f and on the curvatures of Mn+p. Then, we work with the existence and uniqueness of free boundary constant mean curvature hypersurfaces in rotational domains, these are domains whose boundary is generated by a rotation of a graph. We classify the CMC free boundary hypersurfaces as topological disks or annulus, under some conditions in the generatrix function and a gap condition on the umbilicity tensor. Editor: Universidade Federal da Paraíba Tipo: Tese