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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g tori
Description
Morse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that have been 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 a considered map, as it is the subset of its minimal periods.
The dataset consists of 20 files indexed by numbers g=1,...,20. Each file provides all minimal sets of Lefschetz periods for orientation preserving Morse–Smale diffeomorphisms of M(g), an orientable compact surface without boundary of genus g (i.e. a connected sum of g tori).
The data set takes into account not only the algebraical restrictions for the sets of minimal Lefschetz periods that come from zeta functions but also topological ones that can be deduced from the structure of the cohomology ring.
The results are based on the algorithm 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:
- 2020
- Verification date:
- 2021-01-04
- Dataset language:
- English
- Fields of science:
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- mathematics (Natural sciences)
- DOI:
- DOI ID 10.34808/se8g-r382 open in new tab
- Funding:
- Verified by:
- Gdańsk University of Technology
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