A survey of Nielsen periodic point theory (fixed n)
Philip Heath (1999)
Banach Center Publications
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Philip Heath (1999)
Banach Center Publications
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Klaudiusz Wójcik (1999)
Banach Center Publications
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We prove that the Poincaré map has at least fixed points (whose trajectories are contained inside the segment W) where the homeomorphism is given by the segment W.
Zhao, Xuezhi (2008)
Fixed Point Theory and Applications [electronic only]
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Boju Jiang, Seoung Ho Lee, Moo Ha Woo (2004)
Fundamenta Mathematicae
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The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Extending Ferrario's work on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets. Similar formulae for Nielsen type essential orbit numbers are also proved for fibre preserving maps.
Benevieri, Pierluigi, Gavioli, Andrea, Villarini, Massimo (2004)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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J. M. Gambaudo, S. Van Strien, C. Tresser (1989)
Annales de l'I.H.P. Physique théorique
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Evelyn Hart (1999)
Banach Center Publications
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de Carvalho, André, Hall, Toby (2002)
Experimental Mathematics
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Jan Andres, Lech Górniewicz, Marta Lewicka (1996)
Banach Center Publications
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Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.
Lennard Bakker (1999)
Colloquium Mathematicae
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We give a clear and systematic exposition of one-parameter families of brake orbits in dynamical systems on product vector bundles (where the fiber has the same dimension as the base manifold). A generalized definition of a brake orbit is given, and the relationship between brake orbits and periodic orbits is discussed. The brake equation, which implicitly encodes information about the brake orbits of a dynamical system, is defined. Using the brake equation, a one-parameter family of...