Date of Award
Spring 5-15-2014
Document Type
Thesis
Degree Name
Bachelor of Science (BS)
Department
Computing Sciences
College
College of Science
Abstract/Description
The Poincaré recurrence theorem is one of the first and most fundamental theorems of ergodic theory. When applied to a dynamical system satisfying the theorem's hypothesis, it roughly states that the system will, within a finite amount of time, return to a state arbitrarily close to its initial state. This result is intriguing and controversial, providing a contradiction with the Second Law of Thermodynamics known as the recurrence paradox. Here, we treat a set of pool balls on a billiard table as a dynamical system that satisfies the hypotheses of the Poincaré recurrence theorem. We prove that time is a volume-preserving transformation from the state space onto itself. After showing that the hypotheses for the recurrence theorem are met, we discuss the theorem's implications, including possible resolutions of the paradox that arises.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Smith, Aaron, "Applying the Poincaré Recurrence Theorem to Billiards" (2014). Honors Theses. 23.
https://digitalcommons.coastal.edu/honors-theses/23