DSpace Collection:

Weighted composition operators that are chaotic in the sense of Li and Yorke

Tue, 25 Feb 2025 00:00:00 GMT

Title: Weighted composition operators that are chaotic in the sense of Li and Yorke Author(s)/Inventor(s): Vasconcellos, Fernanda Mendonça de Advisor: Bernardes Júnior, Nilson da Costa Abstract: We establish complete characterizations of the notion of Li-Yorke chaos for weighted composition operators on C0(X) spaces and on Lp(μ) spaces (1 ≤ p < ∞). As a consequence, we obtain simple characterizations of the Li-Yorke chaotic weighted shifts on c0 and on ℓp (1 ≤ p < ∞) that complement previously known results. We also investigate the notion of Li-Yorke chaos for weighted shifts on Fr´echet sequence spaces. As applications, we obtain characterizations of the Li-Yorke chaotic weighted shifts on K¨othe sequence spaces depending only on the entries of the K¨othe matrix and the weights of the shift. Publisher: Universidade Federal do Rio de Janeiro Type: Tese

Local and global well-posedness for some dispersive equations in modulation spaces

Tue, 19 Nov 2024 00:00:00 GMT

Title: Local and global well-posedness for some dispersive equations in modulation spaces Author(s)/Inventor(s): Balvin, Fidel Cuba Advisor: Paredes, Xavier Carvajal Abstract: We consider the initial value problem (IVP) associated with a system consisting of modified Korteweg-de Vries (mKdV) type equations ∂tv + ∂3 xv + ∂x(vw2) = 0, v(x, 0) = v0(x), ∂tw + α∂3 xw + ∂x(v2w) = 0, w(x, 0) = w0(x), (3) using the theory of T. Oh and Y. Wang [31] we derive trilinear estimates and use it in the contraction argument, so we prove local well-posedness (LWP) to the IVP (3) for given data in the modulation spaces M2,p s (R) ×M2,p s (R), with s ≥ 1 4 , 2 ≤ p < ∞ and α ̸= 0. Also, at the second part of this work we consider the initial value problem (IVP) associated to the higher order nonlinear Schrödinger (h-NLS) equation with variable coefficients ∂tu + ia(t)∂2 xu + b(t)∂3 xu + ic(t)|u|2u + c1(t)|u|2∂xu = 0, u(x, 0) = u0(x), (4) using the theory of Killip, Visan, Zhang [24], Oh, Wang [30], [31], Carvajal, Gamboa and Santos [8], so we establish a priori estimates and prove global well-posedness (GWP) to the IVP (4) for given data in the modulation spaces M2,p s (R), with s ≥ 1 4 and 2 ≤ p < ∞. Publisher: Universidade Federal do Rio de Janeiro Type: Tese

Um estudo do fenômeno de dissipação anômala em equações de fluidos 2D forçadas

Mon, 23 Dec 2024 00:00:00 GMT

Title: Um estudo do fenômeno de dissipação anômala em equações de fluidos 2D forçadas Author(s)/Inventor(s): Paternina Salgado, David Antonio Advisor: Lopes, Helena Judith Nussenzveig Abstract: In this work, we study the phenomenon of anomalous dissipation of potential enstrophy for the family of Generalized Camassa-Holm equations (GCH) in a two-dimensional periodic domain, which are obtained as an interpolation between second-grade fluid equations and the Camassa-Holm equations. In this context, we first prove the existence and uniqueness of solutions for the GCH equations. Existence is established using the Galerkin method, while for uniqueness, we develop a differential inequality and apply a Grönwall-type inequality.We then demonstrate that for values of β in the range 1/2 < β ≤ 1, there is no anomalous dissipation of potential enstrophy. On the other hand, in the case β = 0, the system exhibits anomalous dissipation of potential enstrophy, specifically infinite dissipation. The analysis of the phenomenon of anomalous dissipation of potential enstrophy was carried out by investigating the inviscid limit of the long-term time averages of the solutions to the GCH equations and subsequently identifying these long-term time averages with stationary statistical solutions in the phase space of potential vorticity. Publisher: Universidade Federal do Rio de Janeiro Type: Tese

Some Properties of ASH attractors

Mon, 24 Mar 2025 00:00:00 GMT

Title: Some Properties of ASH attractors Author(s)/Inventor(s): Pineda Reyes, Miguel Angel Advisor: Arbieto Mendoza, Alexander Eduardo Abstract: This text refers to a doctoral thesis in dynamical systems, which focuses on continuous-time dynamics. More specifically, it advances the theory of asymptotically sectional-hyperbolic (ASH) flows through several fundamental results. First, we prove that every star ASH attractor of a C¹ vector field with positive topological entropy is necessarily sectional-hyperbolic. Second, we establish that all ASH attractors satisfy the intermediate entropy property. Third, we demonstrate that any ASH attractor in three-dimensional vector fields is entropy-expansive and admits periodic orbits. Finally, we provide a lower bound for the growth rate of periodic orbits in an ASH attractor. Publisher: Universidade Federal do Rio de Janeiro Type: Tese