Dynamical Systems and valuations

Resumen:

We introduce the theory of valuations, with special emphasis on its interpretation in terms of Riemann Zariski surfaces, and we will develop the key example of the field of Hardy, corresponding to the real cases. 

We will be consider in the real case, the trajectories of vector fields on R2 y R3, will explore the properties of oscillation and non-oscillation in terms of valuations. We will look to the local uniformization results that are useful in the study of the behavior of the trajectories.

There will be an introduction to the reduction of singularities of dynamic systems, the standardization to the local style of Zariski and there will be some significant demonstrations.

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