Elements of dynamical systems in economy

Many problems in theoretical economics are mathematically formalized as dynamical systems. In recent years a truly open approach to studying the dynamical behavior of these models. That is, economists formulate their hypotheses and study the dynamics of the resulting models rather than formulating the dynamics and studying hypotheses that could lead to models with such dynamics. This is a great progress over using linear models, or using nonlinear models with a linear approach, or even squeezing economic models into well-studied nonlinear systems from other fields. In the following we provide terminology, concepts and examples which are central to understanding the dynamical systems.