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A remark on small divisors problems. (English) Zbl 0419.47029

MSC:
47J05 Equations involving nonlinear operators (general)
54H25 Fixed-point and coincidence theorems (topological aspects)
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References:
[1] В. И. Арнольд: Малые знаменатели и проблемы устойчивости движения в классической и небеской механике. YMH 18, вып. 6 (1963), 91 -192, · Zbl 1145.93303
[2] И. Н. Блинов: Об одном итерационном процессе Ньютона. Изв. АН, сер. мат. 33 (1969), 3-14. · Zbl 1149.62317 · doi:10.2307/2528901 · www.jstor.org
[3] J. Moser: A new technique for the construction of solutions of nonlinear differential equations. Proc. Nat. Acad. Sci. 47 (1961), 1824-1831. · Zbl 0104.30503 · doi:10.1073/pnas.47.11.1824
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[7] V. Pták: Nondiscrete mathematical induction and iterative existence proofs. Linear Algebra and its Applications 13 (1976), 223 - 238. · Zbl 0323.46005 · doi:10.1016/0024-3795(76)90098-7
[8] V. Pták: A modification of Newton’s method. Čas. pěst. mat. 101 (1976), 188-194. · Zbl 0328.46013 · eudml:21271
[9] E. Zehnder: An implicit function theorem for small divisor problems. Bull. Amer. Math. Soc. 50(1974), 174-179. · Zbl 0281.35002 · doi:10.1090/S0002-9904-1974-13407-5
[10] E. Zehnder: Generalized implicit function theorems with applications to some small divisor problems (preprint). · Zbl 0309.58006 · doi:10.1002/cpa.3160280104
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