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:: Volume 6, Issue 2 (Vol. 6, No. 2 2020) ::
Mathematical Researches 2020, 6(2): 151-162 Back to browse issues page
LIMIT AVERAGE SHADOWING AND DOMINATED SPLITTING
Khosro Tajbakhsh Dr *
Tarbiat Modares University , khtajbakhsh@modares.ac.ir
Abstract:   (379 Views)
In this paper the notion of limit average shadowing property is
introduced for diffeomorphisms on a compact smooth manifold M and a class
of diffeomorphisms is given which has the limit average shadowing property,
but does not have the shadowing property. Moreover, we prove that for a
closed f-invariant set Lambda  of a diffeomorphism f, if Lambda is C1-stably limit average
shadowing and the minimal points of  are dense, then Lambda admits a dominated
spiliting.
Keywords: Shadowing, limit averae shadowing, diffeomorphisms, hyperbolicity, dominated splitting.
     
Type of Study: Original Manuscript | Subject: alg
Received: 2018/05/12 | Accepted: 2018/11/28 | Published: 2020/01/28 | ePublished: 2020/01/28
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Tajbakhsh K. LIMIT AVERAGE SHADOWING AND DOMINATED SPLITTING. Mathematical Researches. 2020; 6 (2) :151-162
URL: http://mmr.khu.ac.ir/article-1-2774-en.html


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