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Opis
We consider a closed smooth connected and simply-connected manifold of dimension at least 4 and its self-map f. The topological invariant Dr[f] is equal to the minimal number of r-periodic points in the smooth homotopy class of f. We assume that r is odd and all coefficients b(k) of so-called periodic expansion of Lefschetz numbers of iterations are non-zero for all k dividing r and different from 1. We consider the simplified version of the invariant: Dr[f](mod 1) (which is equal either Dr[f] or Dr[f]+1).
The determination of the exact value of the invariant is a challenging task even for relatively small values of r and low-dimensional manifolds. Nevertheless, in this dataset we are able to provide the estimates for Dr[f](mod 1) for manifolds of dimension between 4 and 21.
We consider an odd r that is a product of 10 prime numbers, each to the power ai, where 1 ≤ i ≤ 10 and 0 ≤ ai ≤ 10. In addition r satisfies the following condition: the number of ai equal to 1 is greater or equal than l (where the dimension of the manifold M is either 2l or 2l+1). The definition of Dr[f](mod 1) and the combinatorial scheme which enables its computation is given in G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84, https://doi.org/10.1007/s11784-012-0076-1].
The data consists of 9 files: dim4_5.txt, dim6_7.txt, dim8_9.txt, dim10_11.txt, dim12_13.txt, dim14_15.txt , dim16_17.txt, dim18_19.txt, dim20_21.txt each of which contains pairs of lists in the form [ai: ai ≠ 0 and 1 ≤ i ≤ 10], [lower_bound, upper_bound], where the first place defines the powers of the prime numbers in the decomposition of r and the second gives the lower and upper bound for the invariant Dr[f](mod 1).
Plik z danymi badawczymi
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} gdzie pojedyncza część pliku jest wielkości 512 MBPrzykładowy skrypt do wyliczenia:
https://github.com/antespi/s3md5
Informacje szczegółowe o pliku
- Licencja:
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otwiera się w nowej karcie
CC BYUznanie autorstwa
Informacje szczegółowe
- Rok publikacji:
- 2020
- Data zatwierdzenia:
- 2020-12-17
- Język danych badawczych:
- angielski
- Dyscypliny:
-
- matematyka (Dziedzina nauk ścisłych i przyrodniczych)
- DOI:
- Identyfikator DOI 10.34808/081x-6069 otwiera się w nowej karcie
- Finansowanie:
- Weryfikacja:
- Politechnika Gdańska
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Powiązane zasoby
- dane badawcze Minimal number of periodic points for smooth self-maps of simply-connected manifolds
- publikacja Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
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