Vacation Scholarship Projects School of Mathematical Sciences Project Titles
نویسندگان
چکیده
This project will study the concept of chaos from a mathematical viewpoint. Qualities which characterise chaos (e.g., sensitive dependence on initial conditions, presence of periodic orbits of all periods, uncountably many aperiodic orbits, and dense orbits) will be studied. Methods for analytically proving that a system is chaotic (presence of a “horseshoe,” intersection of stable and unstable manifolds, Melnikov’s method) will be applied to different systems arising in applications. Prerequisites: a second-year differential equations course.
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