Bolsinov, Alexey V.; Konyaev, Andrey Yu.; Matveev, Vladimir S. Applications of Nijenhuis geometry. V: Geodesic equivalence and finite-dimensional reductions of integrable quasilinear systems. (English) Zbl 07812569 J. Nonlinear Sci. 34, No. 2, Paper No. 33, 18 p. (2024). MSC: 37K05 37K06 37K10 37K25 37K50 53B10 53A20 53B20 53B30 53B50 53B99 53D17 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., J. Nonlinear Sci. 34, No. 2, Paper No. 33, 18 p. (2024; Zbl 07812569) Full Text: DOI arXiv OA License
Bolsinov, Alexey V.; Konyaev, Andrey Yu.; Matveev, Vladimir S. Applications of Nijenhuis geometry. III: Frobenius pencils and compatible non-homogeneous Poisson structures. (English) Zbl 1518.37070 J. Geom. Anal. 33, No. 6, Paper No. 193, 52 p. (2023). MSC: 37K25 37K06 37K10 53D17 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., J. Geom. Anal. 33, No. 6, Paper No. 193, 52 p. (2023; Zbl 1518.37070) Full Text: DOI arXiv
Bolsinov, Alexey V.; Konyaev, Andrey Yu.; Matveev, Vladimir S. Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures. arXiv:2304.10626 Preprint, arXiv:2304.10626 [math.DG] (2023). MSC: 37K05 37K06 37K10 37K25 37K50 53B10 53A20 53B20 53B30 53B50 53B99 53D17 BibTeX Cite \textit{A. V. Bolsinov} et al., ``Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures'', Preprint, arXiv:2304.10626 [math.DG] (2023) Full Text: arXiv OA License
Bolsinov, Alexey V.; Konyaev, Andrey Yu.; Matveev, Vladimir S. Applications of Nijenhuis geometry: non-degenerate singular points of Poisson-Nijenhuis structures. (English) Zbl 1515.37054 Eur. J. Math. 8, No. 4, 1355-1376 (2022). Reviewer: Liviu Popescu (Craiova) MSC: 37J39 37J35 37K25 37K10 53D20 53D17 53D22 70G45 70H06 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., Eur. J. Math. 8, No. 4, 1355--1376 (2022; Zbl 1515.37054) Full Text: DOI arXiv
Bolsinov, Aleksei V.; Veselov, Aleksandr P.; Ye, Yiru Chaos and integrability in \(\operatorname{SL}(2,\mathbb{R})\)-geometry. (English. Russian original) Zbl 1496.37031 Russ. Math. Surv. 76, No. 4, 557-586 (2021); translation from Usp. Mat. Nauk 76, No. 4, 3-36 (2021). MSC: 37D40 37J35 37J39 57M50 57K10 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., Russ. Math. Surv. 76, No. 4, 557--586 (2021; Zbl 1496.37031); translation from Usp. Mat. Nauk 76, No. 4, 3--36 (2021) Full Text: DOI arXiv
Bolsinov, Alexey V.; Konyaev, Andrey Yu; Matveev, Vladimir S. Applications of Nijenhuis geometry. II: Maximal pencils of multi-Hamiltonian structures of hydrodynamic type. (English) Zbl 1475.37075 Nonlinearity 34, No. 8, 5136-5162 (2021). Reviewer: Ivan C. Sterling (St. Mary’s City) MSC: 37K25 37K06 37K10 53D17 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., Nonlinearity 34, No. 8, 5136--5162 (2021; Zbl 1475.37075) Full Text: DOI arXiv Link
Bolsinov, Alexey; Bao, Jinrong A note about integrable systems on low-dimensional Lie groups and Lie algebras. (English) Zbl 1435.37082 Regul. Chaotic Dyn. 24, No. 3, 266-280 (2019). MSC: 37J35 37J37 53B50 70G65 53D17 PDFBibTeX XMLCite \textit{A. Bolsinov} and \textit{J. Bao}, Regul. Chaotic Dyn. 24, No. 3, 266--280 (2019; Zbl 1435.37082) Full Text: DOI
Bolsinov, Alexey V. Complete commutative subalgebras in polynomial Poisson algebras: a proof of the Mischenko-Fomenko conjecture. (English) Zbl 1474.37065 Theor. Appl. Mech. (Belgrade) 43, No. 2, 145-168 (2016). MSC: 37J37 37J35 17B80 70H06 53D17 17B63 PDFBibTeX XMLCite \textit{A. V. Bolsinov}, Theor. Appl. Mech. (Belgrade) 43, No. 2, 145--168 (2016; Zbl 1474.37065) Full Text: DOI arXiv
Bolsinov, A. V.; Konyaev, A. Yu. Algebraic and geometric properties of quadratic Hamiltonians determined by sectional operators. (English. Russian original) Zbl 1317.37068 Math. Notes 90, No. 5, 666-677 (2011); translation from Mat. Zametki 90, No. 5, 689-702 (2011). MSC: 37K10 37K30 70G65 70H06 PDFBibTeX XMLCite \textit{A. V. Bolsinov} and \textit{A. Yu. Konyaev}, Math. Notes 90, No. 5, 666--677 (2011; Zbl 1317.37068); translation from Mat. Zametki 90, No. 5, 689--702 (2011) Full Text: DOI
Bolsinov, A. V.; Oshemkov, A. A. Bi-Hamiltonian structures and singularities of integrable systems. (English) Zbl 1229.37092 Regul. Chaotic Dyn. 14, No. 4-5, 431-454 (2009). MSC: 37K10 37J35 37J20 17B80 PDFBibTeX XMLCite \textit{A. V. Bolsinov} and \textit{A. A. Oshemkov}, Regul. Chaotic Dyn. 14, No. 4--5, 431--454 (2009; Zbl 1229.37092) Full Text: DOI
Bolsinov, Alexey V.; Kiosak, Volodymyr; Matveev, Vladimir S. A Fubini theorem for pseudo-Riemannian geodesically equivalent metrics. (English) Zbl 1175.53022 J. Lond. Math. Soc., II. Ser. 80, No. 2, 341-356 (2009). MSC: 53B10 53B21 53C22 53C50 53D25 70G45 70H06 70H33 58J60 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., J. Lond. Math. Soc., II. Ser. 80, No. 2, 341--356 (2009; Zbl 1175.53022) Full Text: DOI arXiv Link
Bolsinov, A. V.; Dullin, H. R.; Veselov, A. P. Spectra of Sol-manifolds: Arithmetic and quantum monodromy. (English) Zbl 1109.58027 Commun. Math. Phys. 264, No. 3, 583-611 (2006). Reviewer: Roman Srzednicki (Kraków) MSC: 58J50 35P20 37D40 37J35 57M50 58J05 81R12 PDFBibTeX XMLCite \textit{A. V. Bolsinov} et al., Commun. Math. Phys. 264, No. 3, 583--611 (2006; Zbl 1109.58027) Full Text: DOI arXiv Link
Bolsinov, A. V.; Borisov, A. V. Compatible Poisson brackets on Lie algebras. (English. Russian original) Zbl 1042.37041 Math. Notes 72, No. 1, 10-30 (2002); translation from Mat. Zametki 72, No. 1, 11-34 (2002). Reviewer: Rui Loja Fernandes (Lisbon) MSC: 37J35 17B63 53D17 37K30 PDFBibTeX XMLCite \textit{A. V. Bolsinov} and \textit{A. V. Borisov}, Math. Notes 72, No. 1, 10--30 (2002; Zbl 1042.37041); translation from Mat. Zametki 72, No. 1, 11--34 (2002) Full Text: DOI