On attractors of generalized semiflows with impulses

This paper is devoted to the study of global attractors for problems with state-dependent impulses and possible nonuniqueness of solutions. We provide the criteria under which there exists the global attractor, being on one hand an invariant set, and on the other hand given by the difference of the minimal compact attracting set and the impulsive set M. The new condition (T) used to get the global attractor invariance is discussed and compared with other conditions used in literature for impulsive problems. The theory is illustrated by several examples

Weak topological conjugacy via character of recurrence on impulsive dynamical systems

In the present paper, we define the concept of weak topological conjugacy and we establish sufficient conditions to obtain this kind of topological conjugacy between two limit sets. We use the character of recurrence to obtain the results

Attractors for impulsive non-autonomous dynamical systems and their relations

In this work, we deal with several different notions of attractors that may appear in the impulsive non-autonomous case and we explore their relationships to obtain properties regarding the different scenarios of asymptotic dynamics, such as the cocycle attractor, the uniform attractor and the global attractor for the impulsive skew-product semiflow. Lastly, we illustrate our theory by exhibiting an example of a non-classical non-autonomous parabolic equation with subcritical nonlinearity and impulses.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía)Fundação de Amparo à Pesquisa do Estado de São Paul

Impulsive surfaces on dynamical systems

This work is devoted to the construction of impulsive sets in Rn. In the literature, there are many examples of impulsive dynamical systems whose impulsive sets are chosen in an abstract way, and in this paper we present sufficient conditions to characterize impulsive sets in Rn which satisfy some “tube conditions” and ensure a good behavior of the flow. Moreover, we present some examples to illustrate the theoretical results.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía)Fundação de Amparo à Pesquisa do Estado de São Paul

Resumos

ICMC-USPXVII Simpósio de Matemática para a Graduação (SIM).\ud São Carlos, Brasil. 26-28 august 2014

[Book of abstracts]

USPFAPESPCAPESICMC Summer Meeting on Differential Equations (2015 São Carlos

Impulsive semidynamical systems

O objetivo deste trabalho é apresentar um texto, até então inexistente, que compreenda a teoria fundamental dos sistemas semidinâmicos impulsivos. Com este propósito, coletamos resultados de vários artigos e os organizamos dando uma sequência lógica, unificando terminologias e notações e desenvolvendo as demonstrações de forma mais clara e didática do que originalmente apresentadas. Acrescentamos à teoria básica dos sistemas semidinâmicos impulsivos alguns resultados novos sobre conjugação topológica e estabilidade assintótica.The aim of this work is to present a text that encompasses the basis of impulsive semidynamical systems. In view of this, we collected results from various papeis, organized them and unified notations and terminology. We also rewrote the proofs in a more explanatary manner filling the blanks and developing unproved assertions. We contributed to the development of the theory of impulsive semidynamical systems by adding some new results on topologic conjugation and asymptotic stability

The Black-Scholes equation with impulse action

Impulsos são perturbações abruptas que ocorrem em curto espaço de tempo e podem ser consideradas instantâneas. E os mercados financeiros estão sujeitos a choques bruscos como mudanças de governos, quebra de empresas, entre outros. Assim, é natural considerarmos a ação de tais eventos na precificação de ativos financeiros. Nosso objetivo neste trabalho é obtermos uma formulação para a equação diferencial parcial de Black-Scholes com ação impulsiva de modo que os impulsos representem estes choques. Utilizaremos a teoria de integração não-absoluta em espaço de funções para obtenção desta formulaçãoImpulses describe the evolution of systems where the continuous development of a process is interrupted by abrupt changes of state. Financial markets are subject to extreme events or shocks as government changes, companies colapse, etc. Thus it seems natural to consider the action of these events in the valuation of derivative securities. The aim of this work is to obtain a formulation for the Black-Scholes equation with impulse action where the impulses can represent these shocks. We use the non-absolute integration theory in functional spaces to obtain such formulatio

Impulsive semidynamical systems

O objetivo deste trabalho é apresentar um texto, até então inexistente, que compreenda a teoria fundamental dos sistemas semidinâmicos impulsivos. Com este propósito, coletamos resultados de vários artigos e os organizamos dando uma sequência lógica, unificando terminologias e notações e desenvolvendo as demonstrações de forma mais clara e didática do que originalmente apresentadas. Acrescentamos à teoria básica dos sistemas semidinâmicos impulsivos alguns resultados novos sobre conjugação topológica e estabilidade assintótica.The aim of this work is to present a text that encompasses the basis of impulsive semidynamical systems. In view of this, we collected results from various papeis, organized them and unified notations and terminology. We also rewrote the proofs in a more explanatary manner filling the blanks and developing unproved assertions. We contributed to the development of the theory of impulsive semidynamical systems by adding some new results on topologic conjugation and asymptotic stability