کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
839709 1470487 2015 53 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Methods of infinite dimensional Morse theory for geodesics on Finsler manifolds
ترجمه فارسی عنوان
روش های تئوری مورس برای مفهوم بی نهایت برای زمین شناسی بر روی چندفیلد های فینسلر
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
چکیده انگلیسی

We prove the shifting theorems of the critical groups of critical points and critical orbits for the energy functionals of Finsler metrics on Hilbert manifolds of H1H1-curves, and two splitting lemmas for the functionals on Banach manifolds of C1C1-curves. Two results on critical groups of iterated closed geodesics are also proved; their corresponding versions on Riemannian manifolds are based on the usual splitting lemma by Gromoll and Meyer (1969)). Our approach consists in deforming the square of the Finsler metric in a Lagrangian which is smooth also on the zero section and then in using the splitting lemma for nonsmooth functionals that the author recently developed in Lu (2011, 0000, 2013). The argument does not involve finite-dimensional approximations and any Palais’ result in Palais (1966). As an application, we extend to Finsler manifolds a result by V. Bangert and W. Klingenberg (1983) about the existence of infinitely many, geometrically distinct, closed geodesics on a compact Riemannian manifold.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 113, January 2015, Pages 230–282
نویسندگان
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