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Children: Item: Title: 3.1 Solution of the inverse Stäckel problem II for the extended kepler-Coulomb system Item: Title: 3.2 The Stark problem in arbitrary dimension Item: Title: 4 The Stark-Coulomb problem Item: Title: 5 Inverse Stäckel problem II in the Riemann spaces of constant curvature Children: Item: Title: 5.1 The Hamiltonian Stäckel function in the spaces of constant curvature Item: Title: CRediT authorship contribution statement Item: Title: Declaration of competing interest Item: Title: Acknowledgements Item: Title: Data availability Item: Title: References Info: Title: Inverse problems for the Stäckel mechanical systems Author: Jaume Llibre Subject: Physica D: Nonlinear Phenomena, 497 (2026) 135395. doi:10.1016/j.physd.2026.135395 Keywords: Stäckel theorem,Nambu bracket,Inverse problem,Integrability by separation of variables,Korteweg de Vries equation,Stark problem,Pseudo Riemann space of constant curvature,Kepler problem,Homogeneous symmetric polynomial,Levi-Civita 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Physica D: Nonlinear Phenomena, 497 (2026) 135395. doi:10.1016/j.physd.2026.135395 Stäckel theorem Nambu bracket Inverse problem Integrability by separation of variables Korteweg de Vries equation Stark problem Pseudo Riemann space of constant curvature Kepler problem Homogeneous symmetric polynomial Levi-Civita theorem Inverse problems for the Stäckel mechanical systems Jaume Llibre Rafael Ramírez VoR 22nd September 2026 Acrobat Distiller 8.1.0 (Windows) Stäckel theorem,Nambu bracket,Inverse problem,Integrability by separation of variables,Korteweg de Vries equation,Stark problem,Pseudo Riemann space of constant curvature,Kepler problem,Homogeneous symmetric polynomial,Levi-Civita theorem 22nd September 2026 sciencedirect.com elsevier.com true 2010-04-23 10.1016/j.physd.2026.135395 noindex journal 2026-11-01 1 November 2026 10.1016/j.physd.2026.135395 0167-2789 135395 Physica D: Nonlinear Phenomena 135395 https://doi.org/10.1016/j.physd.2026.135395 497 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