Open Access𝐶¹ Connecting Lemmas
Author(s) -
Lan Wen,
Zhihong Xia
Publication year - 2000
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-00-02553-8
Subject(s) - lemma (botany) , algorithm , annotation , computer science , semantics (computer science) , mathematics , artificial intelligence , ecology , poaceae , biology , programming language
Like the closing lemma, the connecting lemma is of fundamental importance in dynamical systems. Hayashi recently proved the C 1 C^1 connecting lemma for stable and unstable manifolds of a hyperbolic invariant set. In this paper, we prove several very general C 1 C^1 connecting lemmas. We simplify Hayashi’s proof and extend the results to more general cases.