A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions

Grzegorz Graff; Alfonso Ruiz-Herrera

doi:10.1007/s10884-013-9345-y

A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions

Abstract

In this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding under the condition of some recurrence properties.

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Grzegorz Graff prof. dr hab.
Alfonso Ruiz-Herrera
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DOI:: Digital Object Identifier (open in new tab) 10.1007/s10884-013-9345-y
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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: Journal of Dynamics and Differential Equations pages 1 - 15,
ISSN: 1040-7294
Language:: English
Publication year:: 2013
Bibliographic description:: Graff G., Ruiz-Herrera A.: A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions// Journal of Dynamics and Differential Equations. -, (2013), s.1-15
DOI:: Digital Object Identifier (open in new tab) 10.1007/s10884-013-9345-y
Verified by:: Gdańsk University of Technology