5 papers
The Complex Spectral Flow: Spectral Conditions for Two-Parameter Equivariant Bifurcation Guarantees
Ziad Ghanem
We introduce the \emph{complex equivariant spectral flow} -- a virtual -representation assembling the eigenvalue winding numbers of the linearization at an isolated two-paramete…
The Ize Conjecture Redux: A Parity Criterion for Global Equivariant Bifurcation Guarantees
Ziad Ghanem
The Ize Conjecture proposed that every absolutely irreducible representation of a compact Lie group admits a maximal isotropy subgroup with an odd-dimensional fixed-point space, wh…
Global Bifurcation of Spiral Wave Solutions to the Complex Ginzburg-Landau Equation
Carlos Garcia-Azpeitia, Ziad Ghanem, Wieslaw Krawcewicz
We use the -equivariant degree to establish the existence of unbounded branches of rotating spiral wave solutions with any number of arms for the complex Ginzburg Land…
Patterns of Non-Stationary Solutions to Symmetric Systems of Second-Order Differential Equations
Ziad Ghanem
We establish the existence of non-stationary solutions to a symmetric system of second-order autonomous differential equations. Our technique is based on the equivariant degree the…
Global Bifurcation in Symmetric Systems of Nonlinear Wave Equations
Carlos Garcia-Azpeitia, Ziad Ghanem, Wieslaw Krawcewicz
In this paper, we use the equivariant degree theory to establish a global bifurcation result for the existence of non-stationary branches of solutions to a nonlinear, two-parameter…