This $297,450 National Science Foundation project grant supports research into hyperbolic dynamical systems with singularities and coexistence of hyperbolic and non-hyperbolic behavior at the University of Houston from August 1, 2022 to July 31, 2025.
The project aims to develop a better understanding of systems displaying hyperbolic behavior in the presence of singularities or coexisting hyperbolic and non-hyperbolic dynamics. Specific activities include studying the properties of such systems and developing tools to rigorously verify this behavior. The research will also provide training for students. Key areas of focus are thermodynamic formalism for billiard systems with singularities, extending previous work on non-uniformly hyperbolic systems to those with singularities, and developing techniques to prove non-uniform hyperbolicity and coexistence in smooth approximations of singular systems. Findings could include constructing a positively curved surface with coexisting hyperbolic and non-hyperbolic geodesic flow. The award supports the NSF's Mathematical and Physical Sciences program to strengthen the nation's scientific enterprise through advancing knowledge in major problems in these fields.
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