Is the Lorenz attractor path-connected?
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Can we tell if the Lorenz attractor is path-connected? By the attractor I do not mean only the line weaving around, but rather its closure.
gn.general-topology ds.dynamical-systems path-connected
edited 1 hour ago
Martin Sleziak
2,96532028
asked 1 hour ago
Douglas SirkDouglas Sirk
112
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add a comment |
$begingroup$
Can we tell if the Lorenz attractor is path-connected? By the attractor I do not mean only the line weaving around, but rather its closure.
gn.general-topology ds.dynamical-systems path-connected
edited 1 hour ago
Martin Sleziak
2,96532028
asked 1 hour ago
Douglas SirkDouglas Sirk
112
New contributor
Douglas Sirk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
2
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You had two chances to spell Lorenz right and you have failed twice :P
$endgroup$
– Wojowu
1 hour ago
add a comment |
$begingroup$
Can we tell if the Lorenz attractor is path-connected? By the attractor I do not mean only the line weaving around, but rather its closure.
gn.general-topology ds.dynamical-systems path-connected
edited 1 hour ago
Martin Sleziak
2,96532028
asked 1 hour ago
Douglas SirkDouglas Sirk
112
New contributor
Douglas Sirk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Can we tell if the Lorenz attractor is path-connected? By the attractor I do not mean only the line weaving around, but rather its closure.
gn.general-topology ds.dynamical-systems path-connected
gn.general-topology ds.dynamical-systems path-connected
edited 1 hour ago
Martin Sleziak
2,96532028
asked 1 hour ago
Douglas SirkDouglas Sirk
112
New contributor
Douglas Sirk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 1 hour ago
Martin Sleziak
2,96532028
asked 1 hour ago
Douglas SirkDouglas Sirk
112
New contributor
Douglas Sirk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 1 hour ago
Martin Sleziak
2,96532028
edited 1 hour ago
Martin Sleziak
2,96532028
edited 1 hour ago
Martin Sleziak
2,96532028
2,96532028
asked 1 hour ago
Douglas SirkDouglas Sirk
112
New contributor
Douglas Sirk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
Douglas SirkDouglas Sirk
112
asked 1 hour ago
Douglas SirkDouglas Sirk
112
112
New contributor
Douglas Sirk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Douglas Sirk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Douglas Sirk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
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You had two chances to spell Lorenz right and you have failed twice :P
$endgroup$
– Wojowu
1 hour ago
add a comment |
2
$begingroup$
You had two chances to spell Lorenz right and you have failed twice :P
$endgroup$
– Wojowu
1 hour ago
2
2
$begingroup$
You had two chances to spell Lorenz right and you have failed twice :P
$endgroup$
– Wojowu
1 hour ago
$begingroup$
You had two chances to spell Lorenz right and you have failed twice :P
$endgroup$
– Wojowu
1 hour ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The question has been answered here: https://mathoverflow.net/a/297836/121665. It is connected but not path connected.
The situation is somewhat similar to the topologist's sine curve: the graph of
$$
f(x)=sinfrac{1}{x},
quad xin (0,1]
$$
is path connected, but its closure (as a subset of $mathbb{R}^2$) is connected, but not path connected.
answered 1 hour ago
Piotr HajlaszPiotr Hajlasz
6,97642457
$endgroup$
$begingroup$
Thank you. I will trust that answer, but I do not really understand it. There is lots of jargon I do not understand. If you could explain a bit of why it is not path-connected I would much appreciate! (or perhaps a reference explaining in detail)
$endgroup$
– Douglas Sirk
57 mins ago
$begingroup$
Also, does "omega-limit set" mean the same thing as "closure" in this context?
$endgroup$
– Douglas Sirk
52 mins ago
add a comment |
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1 Answer
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1 Answer
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active
oldest
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votes
$begingroup$
The question has been answered here: https://mathoverflow.net/a/297836/121665. It is connected but not path connected.
The situation is somewhat similar to the topologist's sine curve: the graph of
$$
f(x)=sinfrac{1}{x},
quad xin (0,1]
$$
is path connected, but its closure (as a subset of $mathbb{R}^2$) is connected, but not path connected.
answered 1 hour ago
Piotr HajlaszPiotr Hajlasz
6,97642457
$endgroup$
$begingroup$
Thank you. I will trust that answer, but I do not really understand it. There is lots of jargon I do not understand. If you could explain a bit of why it is not path-connected I would much appreciate! (or perhaps a reference explaining in detail)
$endgroup$
– Douglas Sirk
57 mins ago
$begingroup$
Also, does "omega-limit set" mean the same thing as "closure" in this context?
$endgroup$
– Douglas Sirk
52 mins ago
add a comment |
$begingroup$
The question has been answered here: https://mathoverflow.net/a/297836/121665. It is connected but not path connected.
The situation is somewhat similar to the topologist's sine curve: the graph of
$$
f(x)=sinfrac{1}{x},
quad xin (0,1]
$$
is path connected, but its closure (as a subset of $mathbb{R}^2$) is connected, but not path connected.
answered 1 hour ago
Piotr HajlaszPiotr Hajlasz
6,97642457
$endgroup$
$begingroup$
Thank you. I will trust that answer, but I do not really understand it. There is lots of jargon I do not understand. If you could explain a bit of why it is not path-connected I would much appreciate! (or perhaps a reference explaining in detail)
$endgroup$
– Douglas Sirk
57 mins ago
$begingroup$
Also, does "omega-limit set" mean the same thing as "closure" in this context?
$endgroup$
– Douglas Sirk
52 mins ago
add a comment |
$begingroup$
The question has been answered here: https://mathoverflow.net/a/297836/121665. It is connected but not path connected.
The situation is somewhat similar to the topologist's sine curve: the graph of
$$
f(x)=sinfrac{1}{x},
quad xin (0,1]
$$
is path connected, but its closure (as a subset of $mathbb{R}^2$) is connected, but not path connected.
answered 1 hour ago
Piotr HajlaszPiotr Hajlasz
6,97642457
$endgroup$
The question has been answered here: https://mathoverflow.net/a/297836/121665. It is connected but not path connected.
The situation is somewhat similar to the topologist's sine curve: the graph of
$$
f(x)=sinfrac{1}{x},
quad xin (0,1]
$$
is path connected, but its closure (as a subset of $mathbb{R}^2$) is connected, but not path connected.
answered 1 hour ago
Piotr HajlaszPiotr Hajlasz
6,97642457
answered 1 hour ago
Piotr HajlaszPiotr Hajlasz
6,97642457
answered 1 hour ago
Piotr HajlaszPiotr Hajlasz
6,97642457
answered 1 hour ago
Piotr HajlaszPiotr Hajlasz
6,97642457
6,97642457
$begingroup$
Thank you. I will trust that answer, but I do not really understand it. There is lots of jargon I do not understand. If you could explain a bit of why it is not path-connected I would much appreciate! (or perhaps a reference explaining in detail)
$endgroup$
– Douglas Sirk
57 mins ago
$begingroup$
Also, does "omega-limit set" mean the same thing as "closure" in this context?
$endgroup$
– Douglas Sirk
52 mins ago
add a comment |
$begingroup$
Thank you. I will trust that answer, but I do not really understand it. There is lots of jargon I do not understand. If you could explain a bit of why it is not path-connected I would much appreciate! (or perhaps a reference explaining in detail)
$endgroup$
– Douglas Sirk
57 mins ago
$begingroup$
Also, does "omega-limit set" mean the same thing as "closure" in this context?
$endgroup$
– Douglas Sirk
52 mins ago
$begingroup$
Thank you. I will trust that answer, but I do not really understand it. There is lots of jargon I do not understand. If you could explain a bit of why it is not path-connected I would much appreciate! (or perhaps a reference explaining in detail)
$endgroup$
– Douglas Sirk
57 mins ago
$begingroup$
Thank you. I will trust that answer, but I do not really understand it. There is lots of jargon I do not understand. If you could explain a bit of why it is not path-connected I would much appreciate! (or perhaps a reference explaining in detail)
$endgroup$
– Douglas Sirk
57 mins ago
$begingroup$
Also, does "omega-limit set" mean the same thing as "closure" in this context?
$endgroup$
– Douglas Sirk
52 mins ago
$begingroup$
Also, does "omega-limit set" mean the same thing as "closure" in this context?
$endgroup$
– Douglas Sirk
52 mins ago
add a comment |
Douglas Sirk is a new contributor. Be nice, and check out our Code of Conduct.
Douglas Sirk is a new contributor. Be nice, and check out our Code of Conduct.
Douglas Sirk is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
You had two chances to spell Lorenz right and you have failed twice :P
$endgroup$
– Wojowu
1 hour ago