On connectedness of chaotic sections of some 3-periodic surfaces

2011/12/26 by Alexandra Skripchenko, Skripchenko, Alexandra · 1 citation
Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #math.GT #msc:37E05 #msc:37E25 #msc:57M99

paper · pdf · doi:10.48550/arxiv.1112.5870

arXiv admin note: substantial text overlap with arXiv:1010.1820

arxiv created 2012/07/05 · arxiv updated 2012/07/06

Abstract

In the present paper we construct a Z³-periodic surface in R³ whose almost all plane sections of a certain direction consist of exactly one connected component. This question originates from a problem of Novikov on the semi- classical motion of an electron in strong magnetic field. Our main tool is the Rips machine algorighm for band complexes.

Citations

• Symmetric interval identification systems of order three

Cited by

• On the Novikov problem for dihedral symmetry potentials

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