Pith Number

pith:XW6MLPEV

pith:2026:XW6MLPEV6TX4IM4UQIEYSFMWAT

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A nonlinear version of the $\alpha$-Kakutani equidistribution problem

Ignacio Rojas

Nonlinear families of C^{1+ε} contractions equidistribute interval endpoints according to Lebesgue measure when nonlattice and thermodynamic regularity conditions hold.

arxiv:2605.16156 v1 · 2026-05-15 · math.DS

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Claims

C1strongest claim

We study a nonlinear version of the problem generated by a finite or countable family of C^{1+ε} contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions.

C2weakest assumption

The family of contractions must satisfy the nonlattice condition together with thermodynamic regularity assumptions; the abstract states these are required for the equidistribution to hold.

C3one line summary

Proves Lebesgue equidistribution of endpoints for nonlinear interval-splitting procedures under nonlattice and thermodynamic regularity assumptions.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Pollicott, M. and Sewell, B. , TITLE =. Israel J. Math. , FJOURNAL =. 2024 , NUMBER =. doi:10.1007/s11856-023-2569-6 , URL = 2024 · doi:10.1007/s11856-023-2569-6

[2] Lalley, S. P. , TITLE =. Acta Math. , FJOURNAL =. 1989 , NUMBER =. doi:10.1007/BF02392732 , URL = 1989 · doi:10.1007/bf02392732

[3] Kesseb\"ohmer, M. and Kombrink, S. , TITLE =. Discrete Contin. Dyn. Syst. Ser. S , FJOURNAL =. 2017 , NUMBER =. doi:10.3934/dcdss.2017016 , URL = 2017 · doi:10.3934/dcdss.2017016

[4] Kakutani, S. , TITLE =. Measure theory (. 1976 , MRCLASS = 1976

[5] Adler, R. L. and Flatto, L. , TITLE =. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete , FJOURNAL =. 1977 , NUMBER =. doi:10.1007/BF00533157 , URL = 1977 · doi:10.1007/bf00533157

Receipt and verification

First computed	2026-05-20T00:01:55.374619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdbcc5bc95f4efc43394820989159604d9789931e0b4fd36ce0505a0963265fa

Aliases

arxiv: 2605.16156 · arxiv_version: 2605.16156v1 · doi: 10.48550/arxiv.2605.16156 · pith_short_12: XW6MLPEV6TX4 · pith_short_16: XW6MLPEV6TX4IM4U · pith_short_8: XW6MLPEV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XW6MLPEV6TX4IM4UQIEYSFMWAT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: bdbcc5bc95f4efc43394820989159604d9789931e0b4fd36ce0505a0963265fa

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-15T16:37:13Z",
    "title_canon_sha256": "f243612887cefca7418f1ff3e5e418f885158a1d53f76a7a715ea5e916daf40a"
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