SMALE established a famous horseshoe model,which shows that there exists a phe-nomenon of chaos in some self-homeomorphisms of discs on the plane although these homeo-morphisms are not very complex.A main conclusion o...SMALE established a famous horseshoe model,which shows that there exists a phe-nomenon of chaos in some self-homeomorphisms of discs on the plane although these homeo-morphisms are not very complex.A main conclusion on the Smale horseshoe is as follows.展开更多
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally f...Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.展开更多
文摘SMALE established a famous horseshoe model,which shows that there exists a phe-nomenon of chaos in some self-homeomorphisms of discs on the plane although these homeo-morphisms are not very complex.A main conclusion on the Smale horseshoe is as follows.
文摘Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
