Cyclic Behavior of Vectors with Non-Zero Orbital Limit Points

Document Type

Grant Proposal

Date Accepted

Summer 2011

Project Description/Abstract

The field of Linear Dynamics was motivated by a problem raised by Von Neumann in the 1940s, which to this day remains unanswered. One of the main concepts in this field relevant to answering this question is that of Chaos, which describes phenomena associated with a precarious alliance between regularity and irregularity. If we imagine a particle moving under the action of a force in a box, we observe that sometimes the particle follows a repetitive pattern in that it simply cycles through a few positions (regularity), while other times it has a completely patternless trajectory and visits the entire box (irregularity). My work with the cyclic behavior of vectors investigates why certain starting positions of a particle yield a trajectory that visits the entire box and others do not. This research will help further our understanding of Linear Dynamics.

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