BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Ale Jan Homburg (University of Amsterdam\, VU University Amsterdam
 )
DTSTART:20230207T130000Z
DTEND:20230207T140000Z
DTSTAMP:20260423T053018Z
UID:OWNS/110
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/110/">I
 terated function systems of linear expanding and contracting maps on the u
 nit interval</a>\nby Ale Jan Homburg (University of Amsterdam\, VU Univers
 ity Amsterdam) as part of One World Numeration seminar\n\n\nAbstract\nWe a
 nalyze the two-point motions of iterated function systems on the unit inte
 rval generated by expanding and contracting affine maps\, where the expans
 ion and contraction rates are determined by a pair $(M\,N)$ of integers.\n
 \nThis dynamics depends on the Lyapunov exponent.\n\nFor a negative Lyapun
 ov exponent we establish synchronization\, meaning convergence of orbits w
 ith different initial points. For a vanishing Lyapunov exponent we establi
 sh intermittency\, where orbits are close for a set of iterates of full de
 nsity\, but are intermittently apart. For a positive Lyapunov exponent we 
 show the existence of an absolutely continuous stationary measure for the 
 two-point dynamics and discuss its consequences.\n\nFor nonnegative Lyapun
 ov exponent and pairs $(M\,N)$ that are multiplicatively dependent integer
 s\, we provide explicit expressions for absolutely continuous stationary m
 easures of the two-point dynamics. These stationary measures are infinite 
 $\\sigma$-finite measures in the case of zero Lyapunov exponent.\n\nThis i
 s joint work with Charlene Kalle.\n
LOCATION:https://researchseminars.org/talk/OWNS/110/
END:VEVENT
END:VCALENDAR