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Relevant bibliographies by topics / Poincaré-Birkhoff theorem

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Journal articles

Academic literature on the topic 'Poincaré-Birkhoff theorem'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Poincaré-Birkhoff theorem"

1

Bonfiglioli, Andrea, and Roberta Fulci. "A New Proof of the Existence of Free Lie Algebras and an Application." ISRN Algebra 2011 (March 7, 2011): 1–11. http://dx.doi.org/10.5402/2011/247403.

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The existence of free Lie algebras is usually derived as a consequence of the Poincaré-Birkhoff-Witt theorem. Moreover, in order to prove that (given a set and a field of characteristic zero) the Lie algebra of the Lie polynomials in the letters of (over the field ) is a free Lie algebra generated by , all available proofs use the embedding of a Lie algebra into its enveloping algebra . The aim of this paper is to give a much simpler proof of the latter fact without the aid of the cited embedding nor of the Poincaré-Birkhoff-Witt theorem. As an application of our result and of a theorem due to Cartier (1956), we show the relationships existing between the theorem of Poincaré-Birkhoff-Witt, the theorem of Campbell-Baker-Hausdorff, and the existence of free Lie algebras.

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2

Michaelis, Walter. "The Dual Poincaré-Birkhoff-Witt Theorem." Advances in Mathematics 57, no. 2 (1985): 93–162. http://dx.doi.org/10.1016/0001-8708(85)90051-9.

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3

Berger, Roland. "The quantum Poincaré-Birkhoff-Witt theorem." Communications in Mathematical Physics 143, no. 2 (1992): 215–34. http://dx.doi.org/10.1007/bf02099007.

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4

Le Calvez, Patrice, and Jian Wang. "Some remarks on the Poincaré-Birkhoff theorem." Proceedings of the American Mathematical Society 138, no. 02 (2009): 703–15. http://dx.doi.org/10.1090/s0002-9939-09-10105-3.

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5

Winkelnkemper, H. E. "A generalization of the Poincaré-Birkhoff theorem." Proceedings of the American Mathematical Society 102, no. 4 (1988): 1028. http://dx.doi.org/10.1090/s0002-9939-1988-0934887-5.

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6

Kirillov, Alexander, and Victor Starkov. "Some extensions of the Poincaré–Birkhoff theorem." Journal of Fixed Point Theory and Applications 13, no. 2 (2013): 611–25. http://dx.doi.org/10.1007/s11784-013-0127-2.

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7

Margheri, Alessandro, Carlota Rebelo, and Fabio Zanolin. "Fixed points for planar maps with multiple twists, with application to nonlinear equations with indefinite weight." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2191 (2021): 20190385. http://dx.doi.org/10.1098/rsta.2019.0385.

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In this paper, we investigate the dynamical properties associated with planar maps which can be represented as a composition of twist maps together with expansive–contractive homeomorphisms. The class of maps we consider present some common features both with those arising in the context of the Poincaré–Birkhoff theorem and those studied in the theory of topological horseshoes. In our main theorems, we show that the multiplicity results of fixed points and periodic points typical of the Poincaré–Birkhoff theorem can be recovered and improved in our setting. In particular, we can avoid assuming area-preserving conditions and we also obtain higher multiplicity results in the case of multiple twists. Applications are given to periodic solutions for planar systems of non-autonomous ODEs with sign-indefinite weights, including the non-Hamiltonian case. The presence of complex dynamics is also discussed. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

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8

Franks, John. "Erratum to “Generalizations of the Poincaré–Birkhoff theorem”." Annals of Mathematics 164, no. 3 (2006): 1097–98. http://dx.doi.org/10.4007/annals.2006.164.1097.

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9

Makar-Limanov, L. "A Version of the Poincaré-Birkhoff-Witt Theorem." Bulletin of the London Mathematical Society 26, no. 3 (1994): 273–76. http://dx.doi.org/10.1112/blms/26.3.273.

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10

Li, Yong, and Zheng Hua Lin. "A constructive proof of the Poincaré-Birkhoff theorem." Transactions of the American Mathematical Society 347, no. 6 (1995): 2111–26. http://dx.doi.org/10.1090/s0002-9947-1995-1290734-4.

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