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Blowing up of the singularity
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Classroom Contents
About Dulac's Problem in R3 for Perturbations of Linear Non-Degenerated Centers
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- 1 Intro
- 2 Fixing notation
- 3 Introduction to Dulac's problem
- 4 Poincaré First Retum map
- 5 An example in
- 6 The local sets of cycles
- 7 Dulac's property for perturbations of linear non degenerated centers
- 8 Blowing up of the (un)stable manifold
- 9 Definition and analyticity of the 1 retum of Poincare
- 10 Conclusions for the semihyperbolic case
- 11 Strategy
- 12 Blowing up of the singularity
- 13 The total transform of the vector field in the coordinate chart C
- 14 Definition of a two dimensional system
- 15 Singularities of the two dimensional system
- 16 Application of the flow boxes to Cu
- 17 Compositions of blowing us
- 18 Final situations
- 19 Invariant surfaces
- 20 The analytic case
- 21 The Poincaré map
- 22 risa curve of fixed points
- 23 Accumulation of cycles in the axis direction
- 24 Final conclusion
