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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
Abstract
Let M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient conditions for a reduction of a set of r-periodic points to one point in the C1-homotopy class.
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- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s10711-016-0199-4
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
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GEOMETRIAE DEDICATA
no. 2016,
pages 1 - 18,
ISSN: 0046-5755 - Language:
- English
- Publication year:
- 2016
- Bibliographic description:
- Graff G., Jezierski J.: Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds// GEOMETRIAE DEDICATA. -Vol. 2016, (2016), s.1-18
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s10711-016-0199-4
- Verified by:
- Gdańsk University of Technology
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