Propriedades dinâmicas em mapeamentos bidimensionais: aplicações em um guia de ondas periodicamente corrugado

• Autor(a) principal: Montero, Leonardo Torres
• Data de Publicação: 2019
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/217448
• topic: Comportamento caótico nos sistemas; Guias de ondas; Sistemas dinâmicos diferenciais; Telecomunicações

Motivated by the growing interest in the study of nonlinear dynamics and chaotic models, in this work we will consider a family of two-dimensional nonlinear mappings that illustrate the dynamics behavior that recovers numerous known problems in different areas such as chemistry, physics, astronomy, mathematics and engineering. When we describe the mapping in the moment and angle variables we can retrieve the model known as corrugated waveguide that describe a beam of light reflected between two mirrors, one of which is smooth and the other is corrugated. Having defined the model, we construct the phase space that illustrates the dynamics of the system, we investigate analytically the position of the first invariant spanning curve in the transition from global chaos to local chaos, using a connection to the standard map. We introduce dissipation into the system and use the Lyapunov exponents to characterize the chaos. From the calculation of the Lyapunov exponents we construct the space of parameters and investigate the periodicity windows in order to analyze the behavior of the periodic structures known as shrimp.