On connectedness of chaotic sections of some 3-periodic surfaces
Abstract
In the present paper we construct a Z^{3}-periodic surface in R^{3} 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2011
- DOI:
- 10.48550/arXiv.1112.5870
- arXiv:
- arXiv:1112.5870
- Bibcode:
- 2011arXiv1112.5870S
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Dynamical Systems;
- 57M99;
- 37E05;
- 37E25
- E-Print:
- arXiv admin note: substantial text overlap with arXiv:1010.1820