The evolution of phase space densities under the action of nonlinear dynamical systems is studied. The identification of macroscopic properties of these systems is made through their corresponding time dependent phase space density state, in close analogy to statistical mechanics. We focus attention on a property that may arise in either deterministic or stochastically perturbed one dimensional maps, known as asymptotic periodicity (AP). Asymptotically periodic systems exhibit an eventual periodicity in the evolution of their phase space densities. The periodic density cycle that emerges is highly sensitive to the initial density of preparation of the system. Three one dimensional systems possessing AP are studied; the hat map, the quadratic map, and noise perturbed Keener maps. Certain physical properties of these maps are derived highlighting their underlying AP. The idea of using a type of entropy, the conditional entropy, as a measure of localization of a cycle of density states of AP systems is discussed.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.59849 |
| Date | January 1990 |
| Creators | Provatas, Nicholas |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001171178, proquestno: AAIMM66477, Theses scanned by UMI/ProQuest. |
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