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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes.
Description
Morse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that were carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of considered map, as it is the subset of its minimal periods.
The dataset consists of 54 files indexed by numbers g=1,...,54. Each file provides all minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms of N(g), a non-orientable compact surface without boundary of genus g (i.e. a connected sum of g real projective planes).
The algorithm for computing the datasets, as well as its justification, are available in the paper: G. Graff, M. Lebiedź, A. Myszkowski, Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms, J. Fixed Point Theory Appl. (2019) 21:47, https://doi.org/10.1007/s11784-019-0680-4.
Dataset file
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} where a single part of the file is 512 MB in size.Example script for calculation:
https://github.com/antespi/s3md5
File details
- License:
-
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CC BYAttribution
Details
- Year of publication:
- 2019
- Verification date:
- 2020-12-17
- Creation date:
- 2018
- Dataset language:
- English
- Fields of science:
-
- mathematics (Natural sciences)
- DOI:
- DOI ID 10.34808/9aj1-1977 open in new tab
- Funding:
- Verified by:
- Gdańsk University of Technology
Keywords
References
- publication Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms
- dataset The database of odd algebraic periods for quasi-unipotent self-maps of a space having the same homology group as the connected sum of g tori
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