Qualitative Differential Equations And Dynamical System
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There are three different windows to study dynamical system, namely: local, global and abstraction. In the local case, one studies the qualitative theory of differential equation in .The main interests are : what does the -limit sets look like ? What happens to the orbits of points in the neighborhood of a fixed point ? Are they stable ?In the global case we study the set of vector fields on manifold such as characterizing the structurally stable vector fields and studying the orbit picture of the flow associated with a given vector field. The last case (Abstraction) will give the view of ideo...
There are three different windows to study dynamical system, namely: local, global and abstraction. In the local case, one studies the qualitative theory of differential equation in .The main interests are : what does the -limit sets look like ? What happens to the orbits of points in the neighborhood of a fixed point ? Are they stable ?In the global case we study the set of vector fields on manifold such as characterizing the structurally stable vector fields and studying the orbit picture of the flow associated with a given vector field. The last case (Abstraction) will give the view of ideological thoughts of motion via. topological transformation group which covers theoretically the other two cases. So, we start with abstraction view, and take a look at topological transformation group which covers the problems that arise in differential equations
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