bibkey: bowen1971entropy
authors: Rufus Bowen
year: 1971
title: Entropy for group endomorphisms and homogeneous spaces
doi: 10.1090/S0002-9947-1971-0274707-X
url: https://doi.org/10.1090/S0002-9947-1971-0274707-X
claim: Classical context for entropy comparison under factor maps and finite-to-one extensions.
strata_touched:
  - D5/S1/Dynamics/FiniteFiberEntropy
license: citation-only
triage: anchor

Entropy for group endomorphisms and homogeneous spaces

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• DOI: https://doi.org/10.1090/S0002-9947-1971-0274707-X (Crossref identifies Transactions of the American Mathematical Society, volume 153, pages 401–414, published 1971).
• The DOI and bibliographic fields were checked against the Crossref work record. No theorem, equation, or page-specific claim is attributed to Bowen beyond the general factor-entropy context stated below.

Bowen’s article appeared in Transactions of the American Mathematical Society, volume 153 (1971), pp. 401–414. This reference acknowledges the classical factor-entropy framework; no novelty is claimed for entropy preservation by uniformly finite-to-one compact factors.

The repository proves its exact compact-uniform-space statement independently: a continuous surjective semiconjugacy, continuous source dynamics, Hausdorff target, and an explicit uniform natural-number bound on finite fibers imply equality of covering entropy. Its block-cover construction bounds the lift cost over r blocks by M^r and sends the entropy cost log(M)/n to zero.

The formal statement includes empty spaces, infinite entropy and a source that need not be Hausdorff. These exact hypotheses and endpoint conventions are supplied by the Lean proof, not asserted to be a literal quotation from Bowen. Bibliographic identity was checked against Crossref; no numbered statement or page-specific quotation from the article is asserted here.