Statistical stability in dynamical systems

Mike Todd (University of St Andrews)

Thursday 14th March 16:00-17:00 Maths 311B


If each member of a continuous family $(f_t)_t$ of dynamical systems possesses a `physical’ measure $\mu_t$ (that is, a measure describing the behaviour of Lebesgue-typical points), one can ask if the family of measures $(\mu_t)_t$ is also continuous in $t$: this is statistical stability, so called because the statistics (for example, in terms of Birkhoff averages for $(f_t, \mu_t)$) change continuously in $t$.  I’ll discuss this problem for interval maps (eg tent maps, quadratic maps).  Statistical stability can be destroyed by topological obstructions, or by a lack of uniform hyperbolicity.  I’ll outline a general theory which guarantees statistical stability, giving examples to show the sharpness of our results. This is joint work with Neil Dobbs (UCD).

Add to your calendar

Download event information as iCalendar file (only this event)