Abstract:
In this talk I will discuss selected properties of generic continuous maps of the interval and circle which preserve the Lebesgue measure. I will focus on a few natural properties such as entropy, structure of periodic points, mixing properties, shadowing properties, etc.
I will also highlight properties of generic maps compared to other possible dynamical behaviors within maps preserving Lebesgue measure.
If time permits, I will present consequences of obtained results for interval maps (not necessarily preserving Lebesgue measure) and two-dimensional dynamics.
(joint work with Jernej Činč, Jozef Bobok and Serge Troubetzkoy)