Difference between Stable, unstable sets , manifolds and subspaces?
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I am confused about the difference between the stable sets, unstable sets ; stable and unstable manifolds; and stable and unstable subspaces of a fixed point $p$ of a map $f : M rightarrow M$ where $M$ is a boundaryless manifold.
Looking at the Wikipedia article, I see the terminology for the words sets and manifolds are used identically here.
terminology dynamical-systems fixedpoints
asked Jan 11 at 21:41
BAYMAXBAYMAX
2,89121123
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add a comment |
$begingroup$
I am confused about the difference between the stable sets, unstable sets ; stable and unstable manifolds; and stable and unstable subspaces of a fixed point $p$ of a map $f : M rightarrow M$ where $M$ is a boundaryless manifold.
Looking at the Wikipedia article, I see the terminology for the words sets and manifolds are used identically here.
terminology dynamical-systems fixedpoints
asked Jan 11 at 21:41
BAYMAXBAYMAX
2,89121123
$endgroup$
2
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Probably what's happening is that if $f$ is "nice" (say, suffuciently differentiable) then the sets are manifolds, and if $f$ is really nice (that is, linear) then the manifods are subspaces.
$endgroup$
– Gerry Myerson
Jan 11 at 22:11
add a comment |
$begingroup$
I am confused about the difference between the stable sets, unstable sets ; stable and unstable manifolds; and stable and unstable subspaces of a fixed point $p$ of a map $f : M rightarrow M$ where $M$ is a boundaryless manifold.
Looking at the Wikipedia article, I see the terminology for the words sets and manifolds are used identically here.
terminology dynamical-systems fixedpoints
asked Jan 11 at 21:41
BAYMAXBAYMAX
2,89121123
$endgroup$
I am confused about the difference between the stable sets, unstable sets ; stable and unstable manifolds; and stable and unstable subspaces of a fixed point $p$ of a map $f : M rightarrow M$ where $M$ is a boundaryless manifold.
Looking at the Wikipedia article, I see the terminology for the words sets and manifolds are used identically here.
terminology dynamical-systems fixedpoints
terminology dynamical-systems fixedpoints
asked Jan 11 at 21:41
BAYMAXBAYMAX
2,89121123
asked Jan 11 at 21:41
BAYMAXBAYMAX
2,89121123
asked Jan 11 at 21:41
BAYMAXBAYMAX
2,89121123
asked Jan 11 at 21:41
BAYMAXBAYMAX
2,89121123
asked Jan 11 at 21:41
BAYMAXBAYMAX
2,89121123
2,89121123
2
$begingroup$
Probably what's happening is that if $f$ is "nice" (say, suffuciently differentiable) then the sets are manifolds, and if $f$ is really nice (that is, linear) then the manifods are subspaces.
$endgroup$
– Gerry Myerson
Jan 11 at 22:11
add a comment |
2
$begingroup$
Probably what's happening is that if $f$ is "nice" (say, suffuciently differentiable) then the sets are manifolds, and if $f$ is really nice (that is, linear) then the manifods are subspaces.
$endgroup$
– Gerry Myerson
Jan 11 at 22:11
2
2
$begingroup$
Probably what's happening is that if $f$ is "nice" (say, suffuciently differentiable) then the sets are manifolds, and if $f$ is really nice (that is, linear) then the manifods are subspaces.
$endgroup$
– Gerry Myerson
Jan 11 at 22:11
$begingroup$
Probably what's happening is that if $f$ is "nice" (say, suffuciently differentiable) then the sets are manifolds, and if $f$ is really nice (that is, linear) then the manifods are subspaces.
$endgroup$
– Gerry Myerson
Jan 11 at 22:11
add a comment |
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Probably what's happening is that if $f$ is "nice" (say, suffuciently differentiable) then the sets are manifolds, and if $f$ is really nice (that is, linear) then the manifods are subspaces.
$endgroup$
– Gerry Myerson
Jan 11 at 22:11