Expansion computed for the quadratic map for different numbers of individual parameters and intervals of parameters using dynamically refined partitions - Open Research Data - MOST Wiedzy

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Expansion computed for the quadratic map for different numbers of individual parameters and intervals of parameters using dynamically refined partitions

Opis

Expansion data computed for the quadratic map by the program that implements the algorithms introduced in the paper “Rigorous computation of expansion in one-dimensional dynamics” by Paweł Pilarczyk, Michał Palczewski and Stefano Luzzatto.

This computation was conducted for 2^n+1 uniformly spaced parameter values in [1.4,2] or for 2^n intervals of parameters of the same size (up to rounding) into which the interval [1.4,2] was split, for n=10,…,17, using dynamically refined partitions of up to 1000 intervals outside the critical neighborhood of radius δ=0.001.

There are several datasets in this package, obtained for the different values of n. The files run20e10.csv through run20e17.csv were obtained for 2^10 through 2^17 intervals of parameters. The files run20e20.csv through run20e27.csv were obtained for 2^10+1 through 2^17+1 individual values of parameters.

The data is in the CSV format, with the first row containing column labels. The contents of the columns is the following:

  • level — the level of subdivision of the parameter interval (e.g. 10 for 2^10=1024 subintervals)
  • num — the identifier of the data piece in the collection at the given subdivision; the identifiers begin with 0
  • parMin — the left endpoint of the parameter interval (minimal parameter value)
  • parMax — the right endpoint of the parameter interval (maximal parameter value)
  • k — the total number of intervals on which the graph representation of the map was built (the critical neighborhood is counted here, too)
  • delta — the radius δ of the critical neighborhood
  • lambda — the computed expansion exponent λ
  • logC — log C if the constant C was computed, otherwise 0
  • lambda0 — the constant λ₀ if it was computed, otherwise 0
  • period — the period of a periodic orbit found (0 if none)
  • lambdaMax — an upper bound on the expansion exponent of the periodic orbit found (0 if none)
  • distFrom0out — the minimum guaranteed distance of the periodic orbit from 0
  • distFrom0in — an upper bound on the distance from 0 during the closest approach to 0
  • compTime — the computation time measured in seconds

This research was supported by the National Science Centre, Poland, within the grant OPUS 2021/41/B/ST1/00405. Some computations were carried out at the Centre of Informatics Tricity Academic Supercomputer & Network.

Plik z danymi badawczymi

run20e10-27.zip
15.9 MB, S3 ETag f71acf0aa3e2f2b3db4361e1237e8e77-1, pobrań: 1
Hash pliku liczony jest ze wzoru
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} gdzie pojedyncza część pliku jest wielkości 512 MB

Przykładowy skrypt do wyliczenia:
https://github.com/antespi/s3md5
pobierz plik run20e10-27.zip

Informacje szczegółowe o pliku

Licencja:
Creative Commons: 0 1.0 otwiera się w nowej karcie
CC 0
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Dane surowe:
Dane zawarte w datasecie nie zostały w żaden sposób przetworzone.

Informacje szczegółowe

Rok publikacji:
2025
Data zatwierdzenia:
2025-05-28
Język danych badawczych:
angielski
Dyscypliny:
  • matematyka (Dziedzina nauk ścisłych i przyrodniczych)
DOI:
Identyfikator DOI 10.34808/3jzq-qk34 otwiera się w nowej karcie
Finansowanie:
Seria:
Weryfikacja:
Politechnika Gdańska

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