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You searched for +publisher:"Penn State University" +contributor:("Mark Levi, Committee Chair/Co-Chair"). One record found.

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Penn State University

1. Hughes, David Rhodri. Entropy of the Lorentz Gas and Other Results.

Degree: 2019, Penn State University

In Chapter 1 we provide relevant definitions and background material on Dynamical Systems and Chaotic Billiards. In Chapter 2 we prove that the topological entropy of the Lorentz gas billiard can take any real positive value if the side lengths of the tables are changed (while the area is held fixed). On the other hand, the metric entropy can take any value between 0 and some constant bound M as the side lengths change. We also show that he ratio of the two entropies can take any value in the interval (0,\frac{1}{2}). It is also shown that both continuously depend on the radius of the circular scatterer. In Chapter 3 we give a new proof of the Gauss-Bonnet Theorem using the inclusion-exclusion formula. In Chapter 4 we show that the ratio of the metric entropy to the topological entropy of the geodesic flow of a surface of negative curvature can be made to take any value in (0,1) by taking a time change of the flow. Finally, in Chapter 5 we have a collection of results on the asymptotic vanishing of the topological entropy of the Bunimovich stadium billiard as the table gets longer and thinner (again, volume is held constant), and that any plane curve homeomorphic to the circle can be recovered from its incidence data with a family of lattices. Advisors/Committee Members: Dmitri Yu Burago, Dissertation Advisor/Co-Advisor, Mark Levi, Committee Chair/Co-Chair, Federico Juan Rodriguez Hertz, Committee Member, Mark Levi, Committee Member, Martin Bojowald, Outside Member.

Subjects/Keywords: Dynamical Systems; Blliards; Entropy

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APA (6th Edition):

Hughes, D. R. (2019). Entropy of the Lorentz Gas and Other Results. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/16864drh272

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Hughes, David Rhodri. “Entropy of the Lorentz Gas and Other Results.” 2019. Thesis, Penn State University. Accessed May 12, 2021. https://submit-etda.libraries.psu.edu/catalog/16864drh272.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Hughes, David Rhodri. “Entropy of the Lorentz Gas and Other Results.” 2019. Web. 12 May 2021.

Vancouver:

Hughes DR. Entropy of the Lorentz Gas and Other Results. [Internet] [Thesis]. Penn State University; 2019. [cited 2021 May 12]. Available from: https://submit-etda.libraries.psu.edu/catalog/16864drh272.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hughes DR. Entropy of the Lorentz Gas and Other Results. [Thesis]. Penn State University; 2019. Available from: https://submit-etda.libraries.psu.edu/catalog/16864drh272

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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