Discrete dynamical systems in solving H-equations

• Main Author: Chen, Jun
• Other Authors: Mathematics
• Format: Others
• Language: en
• Published: Virginia Tech 2014
• Subjects: Chandrasekhar H-equation; LD5655.V856 1995.C446
• Online Access: http://hdl.handle.net/10919/37761; http://scholar.lib.vt.edu/theses/available/etd-05112006-154810/

Three discrete dynamical models are used to solve the Chandrasekhar <i>H</i>-equation with a positive or negative characteristic function. Two of them produce series of continuous functions which converge to the solution of the <i>H</i>-equation. An iteration model of the nth approximation for the <i>H</i>-equation is discussed. This is a nonlinear n-dimensional dynamical system. We study not only the solutions of the nth approximation for the <i>H</i>-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 &#917; (-5.6049, 1] the system has a series of double bifurcation points.For <i>c</i> &#917; ( -8, -5.6049] chaos appears. For <i>c</i> in a window contained the chaos region, a new bifurcation phenomenon is found. For <i>c</i> &#8804;7 any periodic orbits appear. For <i>c</i> in the chaos region the behavior of attractor is discussed. Chaos occurs in the n-dimensional dynamical system. === Ph. D.