C1 interiors of sets of systems with various shadowing properties

Sergei Yu Pilyugin, Kazuhiro Sakai

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийглава/разделрецензирование

1 Цитирования (Scopus)

Аннотация

In this chapter, we study the structure of C1 interiors of some basic sets of dynamical systems having various shadowing properties. We give either complete proofs or schemes of proof of the following main results: • The C1 interior of the set of diffeomorphisms having the standard shadowing property is a subset of the set of structurally stable diffeomorphisms (Theorem 3.1.1); this result and Theorem 1.4.1 (a) imply that the C1 interior of the set of diffeomorphisms having the standard shadowing property coincides with the set of structurally stable diffeomorphisms; • the set Int1.OrientSPF n B/ is a subset of the set of structurally stable vector fields (Theorem 3.3.1); similarly to the case of diffeomorphisms, this result and Theorem 1.4.1 (b) imply that the set Int1.OrientSPF n B/ coincides with the set of structurally stable vector fields; • the set Int1.OrientSPF/ contains vector fields that are not structurally stable (Theorem 3.4.1).

Язык оригиналаанглийский
Название основной публикацииLecture Notes in Mathematics
ИздательSpringer Nature
Страницы125-179
Число страниц55
DOI
СостояниеОпубликовано - 2017

Серия публикаций

НазваниеLecture Notes in Mathematics
Том2193
ISSN (печатное издание)0075-8434

Предметные области Scopus

  • Алгебра и теория чисел

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