Mixing
Invariant cones in Katok-Hasselblatt
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I'm having trouble understanding a lemma presented in Katok & Hasselblatt Introduction to the modern theory of dynamical systems (p.247). Here's the said lemma :
I don't understand the second part of the proof. More specifically, how does it come that if $(u,v) in tilde{V}^gamma_p$, then $Df_m(u,v) = (u',v') in V^gamma_{f_m(p)}$ ?
By definition, we have that $(u,v) in (Df_{m-1})_{f_{m-1}^{-1}(p)} V^gamma_{f_{m-1}^{-1}(p)}$, but I don't see why this implies the conclusion...
Any help is greatly appreciated !
dynamical-systems
asked Jan 9 at 15:47
HermèsHermès
1,710612
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add a comment |
$begingroup$
I'm having trouble understanding a lemma presented in Katok & Hasselblatt Introduction to the modern theory of dynamical systems (p.247). Here's the said lemma :
I don't understand the second part of the proof. More specifically, how does it come that if $(u,v) in tilde{V}^gamma_p$, then $Df_m(u,v) = (u',v') in V^gamma_{f_m(p)}$ ?
By definition, we have that $(u,v) in (Df_{m-1})_{f_{m-1}^{-1}(p)} V^gamma_{f_{m-1}^{-1}(p)}$, but I don't see why this implies the conclusion...
Any help is greatly appreciated !
dynamical-systems
asked Jan 9 at 15:47
HermèsHermès
1,710612
$endgroup$
$begingroup$
I get the feeling something's wrong with notations here...
$endgroup$
– Hermès
Jan 9 at 20:58
add a comment |
$begingroup$
I'm having trouble understanding a lemma presented in Katok & Hasselblatt Introduction to the modern theory of dynamical systems (p.247). Here's the said lemma :
I don't understand the second part of the proof. More specifically, how does it come that if $(u,v) in tilde{V}^gamma_p$, then $Df_m(u,v) = (u',v') in V^gamma_{f_m(p)}$ ?
By definition, we have that $(u,v) in (Df_{m-1})_{f_{m-1}^{-1}(p)} V^gamma_{f_{m-1}^{-1}(p)}$, but I don't see why this implies the conclusion...
Any help is greatly appreciated !
dynamical-systems
asked Jan 9 at 15:47
HermèsHermès
1,710612
$endgroup$
I'm having trouble understanding a lemma presented in Katok & Hasselblatt Introduction to the modern theory of dynamical systems (p.247). Here's the said lemma :
I don't understand the second part of the proof. More specifically, how does it come that if $(u,v) in tilde{V}^gamma_p$, then $Df_m(u,v) = (u',v') in V^gamma_{f_m(p)}$ ?
By definition, we have that $(u,v) in (Df_{m-1})_{f_{m-1}^{-1}(p)} V^gamma_{f_{m-1}^{-1}(p)}$, but I don't see why this implies the conclusion...
Any help is greatly appreciated !
dynamical-systems
dynamical-systems
asked Jan 9 at 15:47
HermèsHermès
1,710612
asked Jan 9 at 15:47
HermèsHermès
1,710612
asked Jan 9 at 15:47
HermèsHermès
1,710612
asked Jan 9 at 15:47
HermèsHermès
1,710612
asked Jan 9 at 15:47
HermèsHermès
1,710612
1,710612
$begingroup$
I get the feeling something's wrong with notations here...
$endgroup$
– Hermès
Jan 9 at 20:58
add a comment |
$begingroup$
I get the feeling something's wrong with notations here...
$endgroup$
– Hermès
Jan 9 at 20:58
$begingroup$
I get the feeling something's wrong with notations here...
$endgroup$
– Hermès
Jan 9 at 20:58
$begingroup$
I get the feeling something's wrong with notations here...
$endgroup$
– Hermès
Jan 9 at 20:58
add a comment |
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$begingroup$
I get the feeling something's wrong with notations here...
$endgroup$
– Hermès
Jan 9 at 20:58