Estimates for minimal number of periodic points for smooth self-maps of simply-connected manifolds|拓扑学数据集|数学分析数据集

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).