Can Brownian motion be regarded as chaos?

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
2
down vote

favorite












I want to know if it is included in chaos. Does it have boundedness, deterministic, initial value sensitivity that is characteristic of chaos?




complex-analysis soft-question brownian-motion nonlinear-system chaos-theory




share|cite|improve this question

























    up vote
    2
    down vote

    favorite












    I want to know if it is included in chaos. Does it have boundedness, deterministic, initial value sensitivity that is characteristic of chaos?




    complex-analysis soft-question brownian-motion nonlinear-system chaos-theory




    share|cite|improve this question























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      I want to know if it is included in chaos. Does it have boundedness, deterministic, initial value sensitivity that is characteristic of chaos?




      complex-analysis soft-question brownian-motion nonlinear-system chaos-theory




      share|cite|improve this question













      I want to know if it is included in chaos. Does it have boundedness, deterministic, initial value sensitivity that is characteristic of chaos?





      complex-analysis soft-question brownian-motion nonlinear-system chaos-theory





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Aug 3 at 17:24
























      asked Aug 3 at 17:01









      Kat

      255




      255




















          1 Answer
          1






          active

          oldest

          votes

















          up vote
          0
          down vote



          accepted










          Perhaps it is related but I wouldn't use the expression "regarded as." Mostly when we talk chaos we are (usually) talking about deterministic dynamical systems. And Brownian motion is a stochastic process.






          share|cite|improve this answer





















          • Stochastic meaning not deterministic.
            – Mason
            Aug 3 at 17:42










          • In fact I'd say it is the opposite of being sensitive to initial conditions. A random walk in 1 or 2 dimensions visits every point in the lattice infinitely often, so in some sense it doesn't matter at all where you start.
            – dbx
            Aug 3 at 18:41










          • @dbx. Not so sure that is a how to interpret sensitivity. It doesn't matter where you start in Lorenz Attractor you'll visit both parts of the system infinitely often. The nature of these trajectories are meaningfully different though... Anyway I recognize that user profile image! Hi! Have you ran a google image search on that profile pic. Any gentleman would find it well worth the time!.
            – Mason
            Aug 3 at 20:55










          • @Mason Is there chaos example in the natural phenomenon?
            – Kat
            Aug 3 at 23:19











          • @Mason Thank you
            – Kat
            Aug 3 at 23:26










          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',
          convertImagesToLinks: true,
          noModals: false,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );








           

          draft saved


          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2871292%2fcan-brownian-motion-be-regarded-as-chaos%23new-answer', 'question_page');

          );

          Post as a guest

















          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          0
          down vote



          accepted










          Perhaps it is related but I wouldn't use the expression "regarded as." Mostly when we talk chaos we are (usually) talking about deterministic dynamical systems. And Brownian motion is a stochastic process.






          share|cite|improve this answer





















          • Stochastic meaning not deterministic.
            – Mason
            Aug 3 at 17:42










          • In fact I'd say it is the opposite of being sensitive to initial conditions. A random walk in 1 or 2 dimensions visits every point in the lattice infinitely often, so in some sense it doesn't matter at all where you start.
            – dbx
            Aug 3 at 18:41










          • @dbx. Not so sure that is a how to interpret sensitivity. It doesn't matter where you start in Lorenz Attractor you'll visit both parts of the system infinitely often. The nature of these trajectories are meaningfully different though... Anyway I recognize that user profile image! Hi! Have you ran a google image search on that profile pic. Any gentleman would find it well worth the time!.
            – Mason
            Aug 3 at 20:55










          • @Mason Is there chaos example in the natural phenomenon?
            – Kat
            Aug 3 at 23:19











          • @Mason Thank you
            – Kat
            Aug 3 at 23:26














          up vote
          0
          down vote



          accepted










          Perhaps it is related but I wouldn't use the expression "regarded as." Mostly when we talk chaos we are (usually) talking about deterministic dynamical systems. And Brownian motion is a stochastic process.






          share|cite|improve this answer





















          • Stochastic meaning not deterministic.
            – Mason
            Aug 3 at 17:42










          • In fact I'd say it is the opposite of being sensitive to initial conditions. A random walk in 1 or 2 dimensions visits every point in the lattice infinitely often, so in some sense it doesn't matter at all where you start.
            – dbx
            Aug 3 at 18:41










          • @dbx. Not so sure that is a how to interpret sensitivity. It doesn't matter where you start in Lorenz Attractor you'll visit both parts of the system infinitely often. The nature of these trajectories are meaningfully different though... Anyway I recognize that user profile image! Hi! Have you ran a google image search on that profile pic. Any gentleman would find it well worth the time!.
            – Mason
            Aug 3 at 20:55










          • @Mason Is there chaos example in the natural phenomenon?
            – Kat
            Aug 3 at 23:19











          • @Mason Thank you
            – Kat
            Aug 3 at 23:26












          up vote
          0
          down vote



          accepted







          up vote
          0
          down vote



          accepted






          Perhaps it is related but I wouldn't use the expression "regarded as." Mostly when we talk chaos we are (usually) talking about deterministic dynamical systems. And Brownian motion is a stochastic process.






          share|cite|improve this answer













          Perhaps it is related but I wouldn't use the expression "regarded as." Mostly when we talk chaos we are (usually) talking about deterministic dynamical systems. And Brownian motion is a stochastic process.







          share|cite|improve this answer













          share|cite|improve this answer



          share|cite|improve this answer











          answered Aug 3 at 17:38









          Mason

          1,1271223




          1,1271223











          • Stochastic meaning not deterministic.
            – Mason
            Aug 3 at 17:42










          • In fact I'd say it is the opposite of being sensitive to initial conditions. A random walk in 1 or 2 dimensions visits every point in the lattice infinitely often, so in some sense it doesn't matter at all where you start.
            – dbx
            Aug 3 at 18:41










          • @dbx. Not so sure that is a how to interpret sensitivity. It doesn't matter where you start in Lorenz Attractor you'll visit both parts of the system infinitely often. The nature of these trajectories are meaningfully different though... Anyway I recognize that user profile image! Hi! Have you ran a google image search on that profile pic. Any gentleman would find it well worth the time!.
            – Mason
            Aug 3 at 20:55










          • @Mason Is there chaos example in the natural phenomenon?
            – Kat
            Aug 3 at 23:19











          • @Mason Thank you
            – Kat
            Aug 3 at 23:26
















          • Stochastic meaning not deterministic.
            – Mason
            Aug 3 at 17:42










          • In fact I'd say it is the opposite of being sensitive to initial conditions. A random walk in 1 or 2 dimensions visits every point in the lattice infinitely often, so in some sense it doesn't matter at all where you start.
            – dbx
            Aug 3 at 18:41










          • @dbx. Not so sure that is a how to interpret sensitivity. It doesn't matter where you start in Lorenz Attractor you'll visit both parts of the system infinitely often. The nature of these trajectories are meaningfully different though... Anyway I recognize that user profile image! Hi! Have you ran a google image search on that profile pic. Any gentleman would find it well worth the time!.
            – Mason
            Aug 3 at 20:55










          • @Mason Is there chaos example in the natural phenomenon?
            – Kat
            Aug 3 at 23:19











          • @Mason Thank you
            – Kat
            Aug 3 at 23:26















          Stochastic meaning not deterministic.
          – Mason
          Aug 3 at 17:42




          Stochastic meaning not deterministic.
          – Mason
          Aug 3 at 17:42












          In fact I'd say it is the opposite of being sensitive to initial conditions. A random walk in 1 or 2 dimensions visits every point in the lattice infinitely often, so in some sense it doesn't matter at all where you start.
          – dbx
          Aug 3 at 18:41




          In fact I'd say it is the opposite of being sensitive to initial conditions. A random walk in 1 or 2 dimensions visits every point in the lattice infinitely often, so in some sense it doesn't matter at all where you start.
          – dbx
          Aug 3 at 18:41












          @dbx. Not so sure that is a how to interpret sensitivity. It doesn't matter where you start in Lorenz Attractor you'll visit both parts of the system infinitely often. The nature of these trajectories are meaningfully different though... Anyway I recognize that user profile image! Hi! Have you ran a google image search on that profile pic. Any gentleman would find it well worth the time!.
          – Mason
          Aug 3 at 20:55




          @dbx. Not so sure that is a how to interpret sensitivity. It doesn't matter where you start in Lorenz Attractor you'll visit both parts of the system infinitely often. The nature of these trajectories are meaningfully different though... Anyway I recognize that user profile image! Hi! Have you ran a google image search on that profile pic. Any gentleman would find it well worth the time!.
          – Mason
          Aug 3 at 20:55












          @Mason Is there chaos example in the natural phenomenon?
          – Kat
          Aug 3 at 23:19





          @Mason Is there chaos example in the natural phenomenon?
          – Kat
          Aug 3 at 23:19













          @Mason Thank you
          – Kat
          Aug 3 at 23:26




          @Mason Thank you
          – Kat
          Aug 3 at 23:26












           

          draft saved


          draft discarded


























           


          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2871292%2fcan-brownian-motion-be-regarded-as-chaos%23new-answer', 'question_page');

          );

          Post as a guest
































































          Comments

          Post a Comment

          Popular posts from this blog

          What is the equation of a 3D cone with generalised tilt?

          Image
          Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an...
          Read more

          Color the edges and diagonals of a regular polygon

          Image
          Clash Royale CLAN TAG #URR8PPP up vote 5 down vote favorite 1 Here is the problem: For what $n$ is it possible to color the edges and diagonals of an $n$-side regular polygon with $dfracbinomn23$ colors, such that you use every color exactly three times and for every color the three segments (edges or diagonals) with that color form a triangle? Trivially $nequiv 0 text or 1 pmod3$. I can also prove that if the statement is true for $k$ than it is true for $3k$ as well. How to finish? Please help! Thanks combinatorial-geometry share | cite | improve this question edited Aug 6 at 21:57 alcana 118 4 asked Aug 6 at 21:15 Leo Gardner 356 11 Even assuming "polyhpn" in the title is a typo for polygon , it is unclear what you mean by "the edges and sides". Aren't the side of a regular polygon the same as the edges? A regular $n$-sided polygon has $n$ edges. – hardmath Aug 6 at 21:20 3 $n$ ne...
          Read more

          Relationship between determinant of matrix and determinant of adjoint?

          Image
          Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). – Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/…...
          Read more