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A Power Geometry and Hypergeometric Functions — arXiv:2609.05474

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.05474
License (as archived): CC0-1.0
Archived: 2026-10-16T15:44:51.062Z
SHA-256 of the archived text: 2ac1de1497d053380fd63e70683020080ecb053f345bf793c4c22693278e245d
Stable URL of this page: https://metraipolis.com/documento/dc_ffb32ffd385c

How to cite

A Power Geometry and Hypergeometric Functions — arXiv:2609.05474 — arXiv (en), https://arxiv.org/abs/2609.05474 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ffb32ffd385c (Metraipolis archive dc_ffb32ffd385c, sha256 2ac1de1497d053380fd63e70683020080ecb053f345bf793c4c22693278e245d)

BibTeX

@misc{dcffb32ffd385c,
  title = {A Power Geometry and Hypergeometric Functions — arXiv:2609.05474},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.05474},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ffb32ffd385c; sha256 2ac1de1497d053380fd63e70683020080ecb053f345bf793c4c22693278e245d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.05474. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper is a corrected English translation of an original Japanese work introducing "power geometry," a research programme centred on power transformations, deformations and dualities of functions in the sense of optimisation theory. Its two main motivations are the origin of probability distributions (via maximum-likelihood principles, rational-function parameters and ODEs linked to information geometry, the Pearson system and Schwarzian equations) and the construction of matrix dynamical systems that compute eigenvalues, singular values and principal or minor subspaces. Building on Brockett's double-bracket flows, the author extends these systems to rectangular matrices, flag manifolds and difference-of-convex potentials, and shows how a continuous power parameter can interpolate between largest- and smallest-eigenvalue problems. Dual potentials, topological distinctions between principal and minor subspace flows, and links via matrix Schwarzian--Riccati equations are examined, with a view toward design principles for classical and quantum information-processing algorithms.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-09 in quant-ph).
Categorie arXiv: Dynamical Systems (math.DS) ; Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.05474 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T15:32:34.887Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).