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SUMMARY:Anton Lukyanenko (George Mason University)
DTSTART:20230418T120000Z
DTEND:20230418T130000Z
DTSTAMP:20260423T035932Z
UID:OWNS/113
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/113/">S
 erendipitous decompositions of higher-dimensional continued fractions</a>\
 nby Anton Lukyanenko (George Mason University) as part of One World Numera
 tion seminar\n\n\nAbstract\nComplex continued fractions (CFs) represent a 
 complex number using a descending fraction with Gaussian integer coefficie
 nts. The associated dynamical system is exact (Nakada 1981) with a piecewi
 se-analytic invariant measure (Hensley 2006). Certain higher-dimensional C
 Fs\, including CFs over quaternions\, octonions\, as well as the non-commu
 tative Heisenberg group can be understood in a unified way using the Iwasa
 wa CF framework (L-Vandehey 2022). Under some natural and robust assumptio
 ns\, ergodicity of the associated systems can then be derived from a conne
 ction to hyperbolic geodesic flow\, but stronger mixing results and inform
 ation about the invariant measure remain elusive. Here\, we study Iwasawa 
 CFs under a more delicate serendipity assumption that yields the finite ra
 nge condition\, allowing us to extend the Nakada-Hensley results to certai
 n Iwasawa CFs over the quaternions\, octonions\, and in $\\mathbb{R}^3$.\n
  \nThis is joint work with Joseph Vandehey.\n
LOCATION:https://researchseminars.org/talk/OWNS/113/
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