Historical presentation · 2019

Families of connected self-similar sets generated by Complex Trees

Bernat Espigulé · 2019-03-28
Topics in Complex Dynamics 2019, IMUB, Universitat de Barcelona
36 slides · Recovered static slides

These static slides were recovered from the original Keynote export, in its original slide order. Animations, embedded video and incremental builds are not reproduced. Extracted text may omit mathematical notation visible in the images. Historical titles and notation are preserved.

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Slide 1: Xavier Jarque & Núria Fagella © Complex Trees bernat@espigule.com Topics in Complex Dynamics 2019 IMUB, Universitat de Barcelona, March 28th Bernat Espigulé arXiv:1902.11

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Xavier Jarque & Núria Fagella © Complex Trees bernat@espigule.com Topics in Complex Dynamics 2019 IMUB, Universitat de Barcelona, March 28th Bernat Espigulé arXiv:1902.11282 Families of connected self-similar sets generated by Complex Trees

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Slide 2: 2014 © Complex Trees Thurston’s last paper Bill Thurston (1946 – 2012) Mathematics is a process of staring hard enough at the fog of confusion to eventually break through

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2014 © Complex Trees Thurston’s last paper Bill Thurston (1946 – 2012) Mathematics is a process of staring hard enough at the fog of confusion to eventually break through to improved clarity. Thurston ENTROPY IN DIMENSION ONE arxiv.org/abs/1402.2008

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Slide 3: © Complex Trees Complex tree Geometric series

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empty string complex-valued alphabet letters complex tree © Complex Trees root nodes tip points word

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tipset complex tree © Complex Trees complex tree

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Slide 6: © Complex Trees First-level pieces The tipset is a self-similar set

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Key idea: “tip-to-tip gluing” © Complex Trees

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Topological set © Complex Trees

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Structurally stable tree Topological set © Complex Trees

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A family of tipset connected trees © Complex Trees

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A family of tipset connected trees © Complex Trees

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A family of tipset connected trees © Complex Trees

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Slide 22: © Complex Trees The unstable set M vs the stable set K

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Slide 29: Family of Binary Complex Trees Related Work: © Complex Trees

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Slide 31: The Wolfram Set W0=W1=M0 © Complex Trees

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Slide 34: @bernatree Holomorphic Dynamics Group Núria Fagella & Xavier Jarque © Complex Trees Bernat Espigulé “If you wish to advance into the infinite, explore the finite in all d

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@bernatree Holomorphic Dynamics Group Núria Fagella & Xavier Jarque © Complex Trees Bernat Espigulé “If you wish to advance into the infinite, explore the finite in all directions.” ⎯ Goethe. Thank you!

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Slide 36: bernat@espigule.com © Complex Trees

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