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Paper   IPM / M / 16947
School of Mathematics
  Title:   Controllability on the infinite-dimensional group of orientation-preserving diffeomorphisms of the unit circle
  Author(s):  Mahdi khajeh Salehani
  Status:   In Proceedings
  Proceeding: Proceedings of the 3rd conference on Dynamical Systems and Geometric Theories
  Year:  2021
  Supported by:  IPM
  Abstract:
In this paper, we give a generalization of Chow-Rashevsky's theorem for control systems in regular connected manifolds modeled on convenient locally convex vector spaces which are not necessarily normable. To indicate an application of our approach to the infinite-dimensional geometric control problems, we conclude with a novel controllability result on the group of orientation-preserving diffeomorphisms of the unit circle, which has applications in, e.g., conformal field theory as well as string theory and statistical mechanics.

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