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dc.contributor.authorMetallo, Steven
dc.date.accessioned2014-09-18T19:32:43Z
dc.date.available2014-09-18T19:32:43Z
dc.date.created2014-05-20
dc.date.issued2014-09-18
dc.identifier.urihttp://hdl.handle.net/123456789/462
dc.description.abstractDynamics is a branch of mathematics that studies how systems change with time, and this can be done using function iteration or di erential equations. Our focus is on the dynamics of the circle map function, fn(x) = nx mod 1, where n is a natural number and the domain is the interval [0; 1] where 0 is identified with 1. This simple function leads to complicated dynamics; it has periodic points of every period as well as in finitely many aperiodic points. We introduce symbolic dynamics by using a Markov partition to split up the domain into intervals with specifi c properties. For Markov partitions, we construct a Markov matrix and prove, through matrix conjugation, that the eigenvalues of the corresponding Markov matrices are 2 and roots of unity.en_US
dc.description.sponsorshipCarthage College Mathematics Departmenten_US
dc.language.isoen_USen_US
dc.subjectCircle Mapsen_US
dc.subjectMarkov Matrixen_US
dc.titleDynamical Systems and Circle Mapsen_US
dc.typeThesisen_US


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