Complex TreesBernat Espigulé

Historical presentation · 2019

Complex Trees: Structural Stability of Connected Self-similar Sets

Bernat Espigulé ·
Illustrating Mathematics, ICERM
40 slides · Recovered static slides

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Slide 11 / 40

Slide 1: Illustrating Mathematics ICERM, Brown University, October 29th bernat@espigule.com Complex Trees: Structural Stability of Connected Self-similar Sets arXiv:1902.11282 Xav
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Illustrating Mathematics ICERM, Brown University, October 29th bernat@espigule.com Complex Trees: Structural Stability of Connected Self-similar Sets arXiv:1902.11282 Xavier Jarque & Núria Fagella Bernat Espigulé

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Slide 2: 2014 Bill Thurston (1946 – 2012) Thurston’s last paper Mathematics is a process of staring hard enough at the fog of confusion to eventually break through to improved cla
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2014 Bill Thurston (1946 – 2012) Thurston’s last paper 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 8: Geometric series Complex tree
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Geometric series Complex tree

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Slide 9: letters word nodes empty string root tip points complex tree complex-valued alphabet
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letters word nodes empty string root tip points complex tree complex-valued alphabet

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Slide 10: tipset complex tree complex tree
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tipset complex tree complex tree

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Slide 11: The tipset is a self-similar set First-level pieces
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The tipset is a self-similar set First-level pieces

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Slide 12: Key idea: “tip-to-tip gluing”
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Key idea: “tip-to-tip gluing”

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Slide 13: Topological set
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Topological set

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Slide 14: Structurally stable tree Topological set
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Structurally stable tree Topological set

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Slide 15: A family of tipset connected trees
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A family of tipset connected trees

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Slide 18: A family of tipset connected trees
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A family of tipset connected trees

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Slide 20: A family of tipset connected trees
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A family of tipset connected trees

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Slide 24: Holomorphic Dynamics Group Núria Fagella & Xavier Jarque Bernat Espigulé Thank you! @bernatree “If you wish to advance into the infinite, explore the finite in all direct
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Holomorphic Dynamics Group Núria Fagella & Xavier Jarque Bernat Espigulé Thank you! @bernatree “If you wish to advance into the infinite, explore the finite in all directions.” ⎯ Goethe.

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

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Slide 35: The unstable set M vs the stable set K
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The unstable set M vs the stable set K

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Slide 39: Symmetric Fractal Trees 
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Symmetric Fractal Trees 

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