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Comstruction of a vector field in $mathbb R^3$ [closed]
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I need to construct a field of vectors in $mathbb R^3$ having two hyperbolic saddles $s_1$, $s_2$, such that:
i) $dim W^u(s_1)=dim W^s(s_2)=2$
ii) $W^u(s_1) ∩ W^s(s_2)$ is transverse along two open orbits $γ_1$ and $γ_2$
iii) $W^s(s_1) ∩ W^u(s_2)$ is an open orbit.
I know it will have a saddle connection. already tried with a paraboloid is a plane like invariant manifolds, but at the intersection would not have an orbit.
dynamical-systems
asked Jul 25 at 15:35
Elismar Dias
43
closed as off-topic by John B, John Ma, Xander Henderson, amWhy, Leucippus Jul 29 at 0:15
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John B, John Ma, Xander Henderson, amWhy, Leucippus
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I need to construct a field of vectors in $mathbb R^3$ having two hyperbolic saddles $s_1$, $s_2$, such that:
i) $dim W^u(s_1)=dim W^s(s_2)=2$
ii) $W^u(s_1) ∩ W^s(s_2)$ is transverse along two open orbits $γ_1$ and $γ_2$
iii) $W^s(s_1) ∩ W^u(s_2)$ is an open orbit.
I know it will have a saddle connection. already tried with a paraboloid is a plane like invariant manifolds, but at the intersection would not have an orbit.
dynamical-systems
asked Jul 25 at 15:35
Elismar Dias
43
closed as off-topic by John B, John Ma, Xander Henderson, amWhy, Leucippus Jul 29 at 0:15
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John B, John Ma, Xander Henderson, amWhy, Leucippus
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I need to construct a field of vectors in $mathbb R^3$ having two hyperbolic saddles $s_1$, $s_2$, such that:
i) $dim W^u(s_1)=dim W^s(s_2)=2$
ii) $W^u(s_1) ∩ W^s(s_2)$ is transverse along two open orbits $γ_1$ and $γ_2$
iii) $W^s(s_1) ∩ W^u(s_2)$ is an open orbit.
I know it will have a saddle connection. already tried with a paraboloid is a plane like invariant manifolds, but at the intersection would not have an orbit.
dynamical-systems
asked Jul 25 at 15:35
Elismar Dias
43
I need to construct a field of vectors in $mathbb R^3$ having two hyperbolic saddles $s_1$, $s_2$, such that:
i) $dim W^u(s_1)=dim W^s(s_2)=2$
ii) $W^u(s_1) ∩ W^s(s_2)$ is transverse along two open orbits $γ_1$ and $γ_2$
iii) $W^s(s_1) ∩ W^u(s_2)$ is an open orbit.
I know it will have a saddle connection. already tried with a paraboloid is a plane like invariant manifolds, but at the intersection would not have an orbit.
dynamical-systems
asked Jul 25 at 15:35
Elismar Dias
43
edited Aug 4 at 0:08
asked Jul 25 at 15:35
Elismar Dias
43
asked Jul 25 at 15:35
Elismar Dias
43
asked Jul 25 at 15:35
Elismar Dias
43
43
closed as off-topic by John B, John Ma, Xander Henderson, amWhy, Leucippus Jul 29 at 0:15
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John B, John Ma, Xander Henderson, amWhy, Leucippus
closed as off-topic by John B, John Ma, Xander Henderson, amWhy, Leucippus Jul 29 at 0:15
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John B, John Ma, Xander Henderson, amWhy, Leucippus
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add a comment |Â
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