Due to the existence of phenomena with chaotic behaviors (quite complicated), where sensitivity to initial conditions is a major obstacle in the studies addressed by the differential equations, H. Until the end of the 19th century, the main approach in the study of dynamical systems was directed to solving analytical or numerical differential equations. The main objective of this area is to understand the asymptotic behavior of the system, given by a transformation or the flow of a differential equation and its orbits.Įrgodic theory is based on general notions of measure theory, and its initial development was motivated by problems in statistical physics. However, they are also considered more general dynamical systems (maps, delay equations, stochastic aspects, etc.).
Dynamical systems are generally described by ordinary differential equations (finite dimensions) or partial differential equations (infinite dimensions). Dynamical Systems appear through all sciences as models for diverse types of phenomena such as the spread of diseases, the climate change system, and satellites’ positioning.
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