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Differential equation x '= Ax h (x) ( where A is the real part of the characteristic roots different from zero ) topological linearization classic conclusion is given by Hartman and Grobman , but their conclusions are local topological linearization requiring homeomorphism function is limited to the origin field . Later , Palmer, K. J extended to non- autonomous systems . Proof , if h (t, x) is bounded, the presence of R ~ n → R ~ n homeomorphism function H, x '= A ( t), XH ( t , x ) of the demapping its linear system Solutions x '= A (t) x , i.e. the global linear. Professor Shi Jinlin removed h (x) bounded limits that when h (x) having an appropriate structure , x ' = Ax H ( x ) can be linearized . His discussion of the equation where f (x), φ (x) allows unbounded . First equation containing only x, non - y which will undoubtedly greatly limits the conclusions of the scope . This study system wherein x ∈ R ~ n, y ∈ R ~ m, A, B , respectively, of order n , m -order matrix , f (x), g (y) , respectively the R ~~ n → the R ~~ n continuous mapping of R ~ m → R ~ n , φ (x ) , φ (y ) respectively and only continuous mapping R ~~ n → R m , R ~~ m → R ~~ m . I.e. allows the first equation with y, thus making the system more general . In this paper, we prove this system when the appropriate conditions are met , the topologically equivalent to its linear system , which greatly expanded the conclusion of the applicable range .
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