On the Dynamic Geometry of Kasner Quadrilaterals with Complex Parameter

Abstract

We explore the dynamics of the sequence of Kasner quadrilaterals (AnBnCnDn)n≥0 defined via a complex parameter α. We extend the results concerning Kasner triangles with a fixed complex parameter obtained in earlier works and determine the values of α for which the generated dynamics are convergent, divergent, periodic, or dense.

Keywords

• dynamical systems
• Kasner quadrilaterals
• convergence
• orbits
• nested quadrilaterals