2 problems

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Classification of smooth endpoint-homogeneous fans by endpoint accumulation invariant
Classification conjecture. If $EPG(F)=EPG(G)\neq\0$ , then $F$ and $G$ are homeomorphic.
Conjectureopencontinuum-theory topological-classification topological-dynamicsarXiv posted 2 days ago
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Continuum of bifurcation-diagram germs in three-parameter families
Continuum conjecture for bifurcation diagrams. There exists an open set in the space of three-parameter families such that the set of pairwise topologically different germs of bifu…
Conjecturerefutedbifurcation-theory dynamical-systems topological-classificationarXiv posted 2 days ago

Classification of smooth endpoint-homogeneous fans by endpoint accumulation invariant