Dissertation > Excellent graduate degree dissertation topics show

Study on Equivariant Bifurcation Problems

Author: GuoRuiZhi
Tutor: LiYangCheng
School: Central South University
Course: Probability Theory and Mathematical Statistics
Keywords: equivariant bifurcation problem contact equivalent group classification recognition left-right equivalent group versal unfolding uniquiness stability
CLC: O212
Type: PhD thesis
Year: 2006
Downloads: 69
Quote: 5
Read: Download Dissertation

Abstract


Ever since the 70s of last century Golubitsky M. and Schaeffer D. G have introduced the idea of applying the methods and techniques of singularity and group theory to the study of bifurcation problems, the bifurcation theory has rapidly developed . The study of bifurcation problems is mainly about how to imply the related concepts and techniques in singularity theory of smooth map germs to bifurcation problems. It includes the following two major aspects:Firstly, the classification and recognition of bifurcation problems. It is a very meaningful but rather difficult subject discussing how many classes bifurcation problems have under some equivalence, what their normal forms are, when a bifurcation problem is equivalent to a given normal form. So we must find the orbital characteristics of these normal forms under the action of some equivalent group. The use of the finite determinacy in singularity theory can transfer infinitely dimensional recognition to finitely dimensional recognition. Modulo high order terms the equivalence group acts as a Lie group on a finitely dimensional space, thus its orbits can be characterized as comprising those germs whose Taylor coefficients satisfy a finite number of polynomial constraints in the form of equalities and inequalities . This characterization is just the solution to the recognition problems. So far the classifications and recognitions of only a few types of bifurcation problems under the condition of low codimensions have beem completed. For example, Keyfitz made the classification of the bifurcations in one state variable, without symmetry up to codimension 7; Golubitsky and Schaeffer obtained the classification of the bifurcation problems in one state variable with Z2 symmetry, in one parameter up to codimension 3; Golubitsky and Roberts studied the classification of degenerate Hopf bifurcation in two state variables with dihedron D4 symmetry, in one parameter up to topological codimension 2; Melbourne obtained the classification of bifurcations in three state variables with octahedral symmetry, in one parameter, up to

Related Dissertations

  1. K Company’s Improving Planning and Forecasting for the Reasonable Allocation of Inventory,F224
  2. The Classification of High Dimsnsion Flew Field Based on Manifold Learning,V231.3
  3. Analysis and Study of Abutment Stability in Concrete High Arch Dam by Three-Dimensional Nonlinear Finite Element Method,TV642.4
  4. The Study on Structural Calculation and Analysis Method of Lattice-type Crane with Variable Cross-section Boom,TH21
  5. Power System Dynamic Voltage Stability Simulation Study Based on Precise Integration Method,TM712
  6. Simulation and Analysis about Switched Reluctance Generator Power Supply System,TM31
  7. Study on the Echo Processing Method for the Measurement of Wire Length Based on Pulsereflection,TM247
  8. Research and Design for the Laser’s Power Control System of Laser Direct Writing,TN249
  9. Multiple ANN/HMM Hybrid Used in Speech Recognition,TN912.34
  10. The Design of a DSP-Based Robot Speech Command Recgnition System,TN912.34
  11. ISAR Imaging Simulation of Space Targets and Target Recognition Based on ISAR Images,TN957.52
  12. The Simulation and Analysis of Spectrum Sensing Based on Higher Order Cumulants,TN911.23
  13. Research on Multi-Sensor Embattling and Continious Tracking Technique Applying for Anti-Stealth and Anti-Interference,TN953
  14. Research on Algorithms of 2D Face Template Protection,TP391.41
  15. Research on the Classification Based on the Reconstruction of Solder Joint,TP391.41
  16. Research on Intelligent Learning-Based Multi-Sensor Target Recognition and Tracking System,TP391.41
  17. The Research and Implementation of Protein Classification Algorithm on the Basic of String Kernel,TP301.6
  18. Research on Image Recognition Algorithm in the Forest Fire Prevention System,TP391.41
  19. Study on Virtual Detector of Infrared Hyper-Spectral Image,TP391.41
  20. Research on Temporal Information Recognition and Normalization,TP391.1
  21. Context-Dependent Lexical Paraphrasing,TP391.1

CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics
© 2012 www.DissertationTopic.Net  Mobile