| Summary: | We explore the dynamics of the sequence of Kasner quadrilaterals <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow><mo>(</mo><msub><mi>A</mi><mi>n</mi></msub><msub><mi>B</mi><mi>n</mi></msub><msub><mi>C</mi><mi>n</mi></msub><msub><mi>D</mi><mi>n</mi></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></semantics></math></inline-formula> defined via a complex parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>. We extend the results concerning Kasner triangles with a fixed complex parameter obtained in earlier works and determine the values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> for which the generated dynamics are convergent, divergent, periodic, or dense.
|
|---|
