Finding topological conjugacy between dynamical systems
$begingroup$
I want to find a topological conjugacy between $x'=lambda x,y'=mu y$ such that $λμ>0$ . Here's my work: I found the solution for both ODEs, given by $x(t)=Me^{lambda t},y(t)=Ne^{mu t}$ for any $M,Ninmathbb{R}$. Then I chose the difeomorphism $h:mathbb{R}tomathbb{R}$ defined by $h(t)=lambda t/mu$. The motivation for this was that $e^{mu h(t)}=e^{lambda t}$. Then, is it true that $x=h^{-1}yh$? I seem to find a problem regarding rhe constants. Furthermore, I suspect that solving the ODEs is not required. Thank you in advance.
general-topology ordinary-differential-equations dynamical-systems
asked Dec 27 '18 at 13:47
Ray BernRay Bern
18013
$endgroup$
add a comment |
$begingroup$
I want to find a topological conjugacy between $x'=lambda x,y'=mu y$ such that $λμ>0$ . Here's my work: I found the solution for both ODEs, given by $x(t)=Me^{lambda t},y(t)=Ne^{mu t}$ for any $M,Ninmathbb{R}$. Then I chose the difeomorphism $h:mathbb{R}tomathbb{R}$ defined by $h(t)=lambda t/mu$. The motivation for this was that $e^{mu h(t)}=e^{lambda t}$. Then, is it true that $x=h^{-1}yh$? I seem to find a problem regarding rhe constants. Furthermore, I suspect that solving the ODEs is not required. Thank you in advance.
general-topology ordinary-differential-equations dynamical-systems
asked Dec 27 '18 at 13:47
Ray BernRay Bern
18013
$endgroup$
$begingroup$
Well, you can check if these two flows commute using this conjugacy. Try to do that first.
$endgroup$
– Evgeny
Dec 27 '18 at 16:01
$begingroup$
Could you please explain what you mean? I'm fairly new to these concepts
$endgroup$
– Ray Bern
Dec 27 '18 at 21:02
add a comment |
$begingroup$
I want to find a topological conjugacy between $x'=lambda x,y'=mu y$ such that $λμ>0$ . Here's my work: I found the solution for both ODEs, given by $x(t)=Me^{lambda t},y(t)=Ne^{mu t}$ for any $M,Ninmathbb{R}$. Then I chose the difeomorphism $h:mathbb{R}tomathbb{R}$ defined by $h(t)=lambda t/mu$. The motivation for this was that $e^{mu h(t)}=e^{lambda t}$. Then, is it true that $x=h^{-1}yh$? I seem to find a problem regarding rhe constants. Furthermore, I suspect that solving the ODEs is not required. Thank you in advance.
general-topology ordinary-differential-equations dynamical-systems
asked Dec 27 '18 at 13:47
Ray BernRay Bern
18013
$endgroup$
I want to find a topological conjugacy between $x'=lambda x,y'=mu y$ such that $λμ>0$ . Here's my work: I found the solution for both ODEs, given by $x(t)=Me^{lambda t},y(t)=Ne^{mu t}$ for any $M,Ninmathbb{R}$. Then I chose the difeomorphism $h:mathbb{R}tomathbb{R}$ defined by $h(t)=lambda t/mu$. The motivation for this was that $e^{mu h(t)}=e^{lambda t}$. Then, is it true that $x=h^{-1}yh$? I seem to find a problem regarding rhe constants. Furthermore, I suspect that solving the ODEs is not required. Thank you in advance.
general-topology ordinary-differential-equations dynamical-systems
general-topology ordinary-differential-equations dynamical-systems
asked Dec 27 '18 at 13:47
Ray BernRay Bern
18013
asked Dec 27 '18 at 13:47
Ray BernRay Bern
18013
asked Dec 27 '18 at 13:47
Ray BernRay Bern
18013
asked Dec 27 '18 at 13:47
Ray BernRay Bern
18013
asked Dec 27 '18 at 13:47
Ray BernRay Bern
18013
18013
$begingroup$
Well, you can check if these two flows commute using this conjugacy. Try to do that first.
$endgroup$
– Evgeny
Dec 27 '18 at 16:01
$begingroup$
Could you please explain what you mean? I'm fairly new to these concepts
$endgroup$
– Ray Bern
Dec 27 '18 at 21:02
add a comment |
$begingroup$
Well, you can check if these two flows commute using this conjugacy. Try to do that first.
$endgroup$
– Evgeny
Dec 27 '18 at 16:01
$begingroup$
Could you please explain what you mean? I'm fairly new to these concepts
$endgroup$
– Ray Bern
Dec 27 '18 at 21:02
$begingroup$
Well, you can check if these two flows commute using this conjugacy. Try to do that first.
$endgroup$
– Evgeny
Dec 27 '18 at 16:01
$begingroup$
Well, you can check if these two flows commute using this conjugacy. Try to do that first.
$endgroup$
– Evgeny
Dec 27 '18 at 16:01
$begingroup$
Could you please explain what you mean? I'm fairly new to these concepts
$endgroup$
– Ray Bern
Dec 27 '18 at 21:02
$begingroup$
Could you please explain what you mean? I'm fairly new to these concepts
$endgroup$
– Ray Bern
Dec 27 '18 at 21:02
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3053943%2ffinding-topological-conjugacy-between-dynamical-systems%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3053943%2ffinding-topological-conjugacy-between-dynamical-systems%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Well, you can check if these two flows commute using this conjugacy. Try to do that first.
$endgroup$
– Evgeny
Dec 27 '18 at 16:01
$begingroup$
Could you please explain what you mean? I'm fairly new to these concepts
$endgroup$
– Ray Bern
Dec 27 '18 at 21:02