Pith Number

pith:D52RAPAR

pith:2026:D52RAPARGMXD5I2IQEUE7ZDB3L

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Integrability of oscillators and transcendental invariant curves

Dmitry Sinelshchikov, Jaume Gin\'e

Transcendental invariant curves with polynomial or rational cofactors yield first integrals for non-Liouvillian integrable oscillators.

arxiv:2605.15977 v1 · 2026-05-15 · nlin.SI · math.DS

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Claims

C1strongest claim

We demonstrate that this approach can be efficiently used for finding non-Liouvillian and non-Puiseux integrable dynamical systems... We illustrate this approach by proving non-Liouvillian integrability of two dynamical systems from the Painlevé–Gambier classification and non-Puiseux integrability of an oscillator from the considered family.

C2weakest assumption

The method assumes that the relevant transcendental invariant curves exist and that their cofactors being polynomial or rational in one variable is sufficient to reduce the search to linear algebraic and linear ODE problems whose solutions yield the integrals.

C3one line summary

A method based on transcendental invariant curves with polynomial or rational cofactors is used to prove integrability for selected nonlinear oscillators and Painlevé-Gambier systems by solving linear algebraic and ODE problems.

References

59 extracted · 59 resolved · 0 Pith anchors

[1] Dove r Publications, New York (2011) 2011

[2] Murray, J.D.: Mathematical Biology. I. An Introduction. Springe r-Verlag, Berlin, Heidelberg (2001) 2001

[3] MIT press ( 2007) 2007

[4] Jenkins, A.: Self-oscillation. Phys. Rep. 525, 167–222 (2013) 2013

[5] Ghosh, S., Ray, D.S.: Chemical oscillator as a generalized Rayleigh os cillator. J. Chem. Phys. 139, 164112 (2013) 2013

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:47.366626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f75103c11332e3ea34881284fe461dad145b3695162892311e92e4fbb013853

Aliases

arxiv: 2605.15977 · arxiv_version: 2605.15977v1 · doi: 10.48550/arxiv.2605.15977 · pith_short_12: D52RAPARGMXD · pith_short_16: D52RAPARGMXD5I2I · pith_short_8: D52RAPAR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/D52RAPARGMXD5I2IQEUE7ZDB3L \
  | 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: 1f75103c11332e3ea34881284fe461dad145b3695162892311e92e4fbb013853

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "1b7d598da2a5ffb05711a0314f8080c9b9c227e9e02c006a7a6c3ca43e61743b",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.SI",
    "submitted_at": "2026-05-15T14:11:49Z",
    "title_canon_sha256": "99504a0c58e84567427ee5d9b225b582e3242cdec630afac881190646e126c28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15977",
    "kind": "arxiv",
    "version": 1
  }
}