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Unsmoothable Diffeomorphisms

Aledarvish, Ali | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53121 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Sharifitabar, Mohsen; Nassiri, Mesam
  7. Abstract:
  8. The primary goal of this thesis is to study dynamics with maximum degree of smoothness that can not be smoother with topological conjugacy. In chapter one it will show existence of such dynamics for r to be integer and dimension two. In the next chapter we extend the result to any dimension and we prove there is a relation between maximum smoothness degree of given map and it’s topological properties. In the last chapter we turn to hyperbolic dynamics and bifurcation theory and present a completely different example of such maps in dimension two in the Newhouse domain which is open subset of Cr diffeomorphisms
  9. Keywords:
  10. Unsmoothable Diffeomorphisms ; Newhouse Domian ; Inherent Differentiability ; Dynamics with Maximum Degree of Smoothness ; Topological Conjugacy

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