Bifurcation and Symmetry: Cross Influence Between Mathematics and Applications

ISBN-13: 9783034875387 / Angielski / Miękka / 2013 / 327 str.

Bohmer;Allgower;Golubitsky

Opis

Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre- sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps- University of Marburg, Germany.

Spis treści

Exploiting Equivariance in the Reduced Bifurcation Equations.- The Homoclinic Twist Bifurcation Point.- High Corank Steady-State Mode Interaction on a Rectangle.- Numerical Investigation of the Bifurcation from Travelling Waves to Modulated Travelling Waves.- Mode Interactions of an Elliptic System on a Square.- Secondary, Tertiary and Quaternary States of Fluid Flow.- Hopf-type Bifurcations in the presence of Linear and Nonlinear Symmetries.- On Diffusively Coupled Oscillators.- Mechanisms of Symmetry Creation.- Generic Bifurcation of Pendula.- Symmetry Aspects of 3-Periodic Minimal Surfaces.- Hopf Bifurcation at Non-semisimple Eigenvalues: A Singularity Theory Approach.- Trigonometric Collocation in Hopf Bifurcation.- Exploiting Symmetry in Solving Linear Equations.- Symmetry and Preservation of Nodal Structure in Elliptic Equations Satisfying Fully Nonlinear Neumann Boundary Conditions.- A New Approach for Solving Singular Nonlinear Equations.- Quasiperiodic Drift Flow in the Couette-Taylor Problem.- Numerical Applications of Equivariant Reduction Techniques.- Numerical Bifurcation Analysis of a Model of Coupled Oscillators.- Numerical Exploration of Bifurcations and Chaos in Coupled Oscillators.- Hopf bifurcation with Z4 x T2 Symmetry.- Forced Symmetry Breaking from O(3).- Utilization of Scaling Laws and Symmetries in the Path Following of a Semilinear Elliptic Problem.- Linear Stability of Axisymmetric Thermocapillary Convection in Crystal Growth.- An Indirect Approach to Computing Origins of Hopf Bifurcations and its Applications to Problems with Symmetry.- A Version of GMRES for Nearly Symmetric Linear Systems.- Hopf/Steady-state Mode Interaction for a Fluid Conveying Elastic Tube with D4-Symmetric Support.- Test Functions for Bifurcation Points and Hopf Points in Problems with Symmetries.