N. Ladis and Kuiper gave the classification of the topological equivalence of linear autonomous system. More precisely, they proved if two linear autonomous system $\dot{X}= AX, \dot{X}= BX$ are topologically equivalent, where $X\in \mathbb{R}^n$ and $A, B$ are real $n\times n$ matrices, then $A, B$ must satisfy some algebraic condition(which I do not want to state because it is a little bit long, but it only depends on the algebraic property(like Jordan form etc) of the matrices $A, B$). My question is those two articles are hard to found, is there reference book or paper giving the proof in details? Thanks.
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$\begingroup$ It should be in Robinson's book "Dynamical Systems: Stability, Symbolic Dynamics, and Chaos". An online source is section 2.3.3 of cs.elte.hu/~simonp/dynsysdiffeq.pdf which gives a complete proof. $\endgroup$– ThiKuCommented Dec 25, 2016 at 5:34
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$\begingroup$ I checked Robinson's book, it only dealt with hyperbolic case, similar for Simon's lecture notes, so far it seems that there is not details proof except Ladis or Kuiper's papers on this. $\endgroup$– mmaatthhCommented Dec 25, 2016 at 9:10
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$\begingroup$ Now I'm curious about this condition. Could you state it? It would make your question more useful, at least. $\endgroup$– Jairo BochiCommented Dec 25, 2016 at 14:04
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1$\begingroup$ @ Jairo Bochi, the condition is the dimension of generalized eigenspace of $A$ with respect to eigenvalues, whose real part is positive (negative), must be equal to the dimension of generalized eigenspace of $B$ with respect to eigenvalues, whose real part is positive (negative). And the generalized eigenspace of $A$ with respect to eigenvalues, whose real part is $0$, denoted as $W_0(A)$, $A|_{W_0(A)}$ is linearly equivalent to $B_{W_0(B)}$, where $W_0(B)$ is defined similarly as $W_0(A)$. $\endgroup$– mmaatthhCommented Dec 27, 2016 at 0:46
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