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…
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…
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…