Expansion computed for the quadratic map for 65537 parameters using dynamically refined partitions into up to 2000 intervals - Open Research Data - Bridge of Knowledge

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Expansion computed for the quadratic map for 65537 parameters using dynamically refined partitions into up to 2000 intervals

Description

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 2^16+1 = 65537 uniformly spaced parameter values in [1.4,2] using dynamically refined partitions of up to 2000 intervals outside the critical neighborhood of radius δ=0.001.

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.

Dataset file

lambdaMax.csv
6.6 MB, S3 ETag 3981e86b468ef84480553118223e6fa8-1, downloads: 0
The file hash is calculated from the formula
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:
Creative Commons: 0 1.0 open in new tab
CC 0
Public Domain Dedication
Raw data:
Data contained in dataset was not processed.

Details

Year of publication:
2025
Verification date:
2025-05-28
Dataset language:
English
Fields of science:
  • mathematics (Natural sciences)
DOI:
DOI ID 10.34808/sq4h-5890 open in new tab
Funding:
Series:
Verified by:
Gdańsk University of Technology

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