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Non-statistical Dynamical Systems

Talebi, Aminosadat | 2023

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 55991 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Razvan, Mohammad Reza; Nassiri, Meysam; Berger, Pierre
  7. Abstract:
  8. Non-statistical dynamics are those dynamical systems for which a large subset of points in the phase space (positive measure subset) have non-statistical behavior, meaning that the orbit of these points does not have asymptotic distribution in the phase space. We introduce two new classes of these kinds of dynamics: non-statistical rational maps on the Reimann sphere and non-statistical Anosov-Katok maps of the annulus. We then give a general formalization of the notion of "statistical (in)stability" and show how it is connected to the existence of non-statistical dynamics in a general family of maps
  9. Keywords:
  10. Statistical Stability ; Anosov-Katok Maps ; Rational Maps ; Non-Statistical Dynamical Systems

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