On the Dynamic Geometry of Kasner Quadrilaterals with Complex Parameter

Dorin Andrica, Ovidiu Bagdasar

Type: Article

Publication Date: 2022-09-14

Citations: 1

DOI: https://doi.org/10.3390/math10183334

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.

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Works Cited by This (11)

Action	Title	Year	Authors
+ PDF Chat	Markov chains and dynamic geometry of polygons	2003	Jiu Ding L. R. Hitt Xin-Min Zhang
+	On Sequences of Nested Triangles	2006	Dan Ismailescu Jacqueline J.L. Jacobs
+ PDF Chat	Dynamic Geometry of Polygons	2001	L. R. Hitt Xinmin Zhang
+	Sequences of Polygons	1979	R.J. Clarke
+	Iterative Processes in Elementary Geometry	1983	Gengzhe Chang Philip J. Davis
+ PDF Chat	Polygons and iteratively regularizing affine transformations	2016	Otto Roeschel
+	On the Characterization of Periodic Complex Horadam Sequences	2013	Ovidiu Bagdasar Peter J. Larcombe
+	Polygons derived from polygons via iterated constructions	2016	Serena Donisi Martini Horst Gaetano Vitale Giovanni Vincenzi
+	80.2 Averaging sequences and triangles	1996	Steve Abbott
+	The Sequence of Pedal Triangles	1988	J. G. Kingston J. L. Synge