ABSTRACT
This chapter focuses on dynamical systems in the plane It begins by reviewing some important ideas from linear algebra and multivariable calculus that provide a foundation for studying dynamics in R. The relationship between a matrix and a linear transformation is a little bit more complicated. The chapter describes the process of understanding the dynamical similarities and differences of linear systems with complex eigenvalues as compared to those with real eigenvalues. It briefly introduces the chaos part of the story as that most closely parallels the study of one-dimensional dynamics. The story of chaotic dynamics in the plane begins with a closer look at saddle fixed points.
