Dynamics Of R-L-Diode System

In this thesis, we discuss the piecewise linear model which is generated from a R-L-Diode Driven circuit in Physics. Some topological and symbolic properties are presented.In section 2, we study the fixed point, stable set and unstable set of this system. For given parameters a trapping region is found with the property that any interval of unstable set will be expand under the map, So we get the conclusion that the system has infinitely many homoclinic orbits.As a consequence of the previous conclusion, we discuss the attractor of the system. The proof of the existence of a topologically transitive attractor is given.In section 4, we symbolized the system using Milnor-Thurston's method. We not only define the map from plane to symbolic space, also define its inverse map x0,-1 which maps symbolic space to plane. So we associate the symbolic space {+1,-1}Z with the plain R2. The conclusion is that any two sequences which have the same heads (resp. tails) sequences will be mapped to the same line under the map x0, -1Based on this result, we introduced the pruning front and the primary pruned region. The proof of pruning front conjecture is given in section 5.Finally, we discuss some problems for further study.