In 1970s Bowen related hyperbolic dynamics with specification property and used this to show that there exists a unique measure of maximal entropy. Almost the same time Sigmund used specification property as a tool in characterization of simplex of invariant measures. Since then, these results were inspiration for numerous mathematicians in various studies of dynamics. Several weaker versions of specification property were developed and used as a tool for better understanding of dynamics. At the same time, questions, how often such properties can be found in dynamics were raised (e.g. in the sense of Baire category theorem).

In this talk we will present selected questions and results fitting into the above framework of research.
Meeting ID: 852 4277 3200 Passcode: 103121