Discrete dynamical systems in solving H-equations

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dc.contributor.authorChen, Junen
dc.contributor.committeecochairBowden, Robert L.en
dc.contributor.committeecochairGreenberg, Williamen
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberLin, Taoen
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:10:54Zen
dc.date.adate2006-05-11en
dc.date.available2014-03-14T21:10:54Zen
dc.date.issued1995-08-17en
dc.date.rdate2006-05-11en
dc.date.sdate2006-05-11en
dc.description.abstractThree discrete dynamical models are used to solve the Chandrasekhar H-equation with a positive or negative characteristic function. Two of them produce series of continuous functions which converge to the solution of the H-equation. An iteration model of the nth approximation for the H-equation is discussed. This is a nonlinear n-dimensional dynamical system. We study not only the solutions of the nth approximation for the H-equation but also the mathematical structure and behavior of the orbits with respect to the parameter function, i.e. characteristic function. The dynamical system is controlled by a manifold. For n=2, stability of the fixed points is studied. The stable and unstable manifolds passing through the hyperbolically fixed point are obtained. Globally, the bounded orbits region is given. For parameter c in some region a periodic orbit of one dimension will cause periodic orbits in the higher dimensional system. For changing parameter c, the bifurcation points are discussed. For c ∈ (-5.6049, 1] the system has a series of double bifurcation points. For c ∈ (-8, -5.6049] chaos appears. For c in a window contained the chaos region, a new bifurcation phenomenon is found. For c ≤ -7 any periodic orbits appear. For c in the chaos region the behavior of attractor is discussed. Chaos occurs in the n-dimensional dynamical system.en
dc.description.degreePh. D.en
dc.format.extentv, 95 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-05112006-154810en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05112006-154810/en
dc.identifier.urihttp://hdl.handle.net/10919/37761en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1995.C446.pdfen
dc.relation.isformatofOCLC# 33433282en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectChandrasekhar H-equationen
dc.subject.lccLD5655.V856 1995.C446en
dc.titleDiscrete dynamical systems in solving H-equationsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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