Symbolic dynamics in continue dynamical system
0
$begingroup$
Do you know a good and studied example of symbolic dynamics applied to a continue dynamical system? I mean, if there is an example of a continue dynamical system for which there is a Poincaré map for which there is an invariant set conjugated to the space of $N$ symbols with the shift operator.
And, if there is, one or more books where i can find it.
dynamical-systems
edited Nov 27 '18 at 16:30
John B
12.2k51840
asked Nov 27 '18 at 15:19
tommycauterotommycautero
867
$endgroup$
add a comment |
0
$begingroup$
Do you know a good and studied example of symbolic dynamics applied to a continue dynamical system? I mean, if there is an example of a continue dynamical system for which there is a Poincaré map for which there is an invariant set conjugated to the space of $N$ symbols with the shift operator.
And, if there is, one or more books where i can find it.
dynamical-systems
edited Nov 27 '18 at 16:30
John B
12.2k51840
asked Nov 27 '18 at 15:19
tommycauterotommycautero
867
$endgroup$
$begingroup$
Great starting point: projecteuclid.org/euclid.acta/1485890097
$endgroup$
– John B
Nov 27 '18 at 16:30
$begingroup$
Thank you, but this is too much difficult for me (I mean, objects used in that paper, like for example Fuchsian groups, which i have never heard about, doesn't allow me to read and understand this without before reading lot of literature concerning other field of mathematics and other definitions). I found the "strange attractor" in the Lorenz system can be what i was looking for; in Robert Devaney, Morris W. Hirsch - "Differential equations, dynamical systems, and an introduction to chaos" it seems that it's explained with basic calculus facts and without any new definition. Thanks anyway
$endgroup$
– tommycautero
Nov 27 '18 at 17:35
$begingroup$
I understand, I didn't know your background. A minor word of caution, if I may: the Lorenz system has associated a hyperbolic system with singularities, which is not really what you want, at least from your question. This corresponds to the fact that in Figure 14.10 in that book (by Hirsch, Smale and Devaney) the two parts of the graph are not onto. Without exaggeration, this makes the situation atypical from the usual one, and you may be studying a different thing from what you want to study.
$endgroup$
– John B
Nov 27 '18 at 17:54
$begingroup$
yes i know, it's not exactly what I wanted, but the chaotic nature was the main thing i was looking for, not necessary with cantor sets or symbolic dynamics. Maybe I express myself a little wrong before. Thanks a lot for the advice, have a nice day:)
$endgroup$
– tommycautero
Nov 27 '18 at 18:01
add a comment |
0
0
0
$begingroup$
Do you know a good and studied example of symbolic dynamics applied to a continue dynamical system? I mean, if there is an example of a continue dynamical system for which there is a Poincaré map for which there is an invariant set conjugated to the space of $N$ symbols with the shift operator.
And, if there is, one or more books where i can find it.
dynamical-systems
edited Nov 27 '18 at 16:30
John B
12.2k51840
asked Nov 27 '18 at 15:19
tommycauterotommycautero
867
$endgroup$
Do you know a good and studied example of symbolic dynamics applied to a continue dynamical system? I mean, if there is an example of a continue dynamical system for which there is a Poincaré map for which there is an invariant set conjugated to the space of $N$ symbols with the shift operator.
And, if there is, one or more books where i can find it.
dynamical-systems
dynamical-systems
edited Nov 27 '18 at 16:30
John B
12.2k51840
asked Nov 27 '18 at 15:19
tommycauterotommycautero
867
edited Nov 27 '18 at 16:30
John B
12.2k51840
asked Nov 27 '18 at 15:19
tommycauterotommycautero
867
edited Nov 27 '18 at 16:30
John B
12.2k51840
edited Nov 27 '18 at 16:30
John B
12.2k51840
edited Nov 27 '18 at 16:30
John B
12.2k51840
12.2k51840
asked Nov 27 '18 at 15:19
tommycauterotommycautero
867
asked Nov 27 '18 at 15:19
tommycauterotommycautero
867
asked Nov 27 '18 at 15:19
tommycauterotommycautero
867
867
$begingroup$
Great starting point: projecteuclid.org/euclid.acta/1485890097
$endgroup$
– John B
Nov 27 '18 at 16:30
$begingroup$
Thank you, but this is too much difficult for me (I mean, objects used in that paper, like for example Fuchsian groups, which i have never heard about, doesn't allow me to read and understand this without before reading lot of literature concerning other field of mathematics and other definitions). I found the "strange attractor" in the Lorenz system can be what i was looking for; in Robert Devaney, Morris W. Hirsch - "Differential equations, dynamical systems, and an introduction to chaos" it seems that it's explained with basic calculus facts and without any new definition. Thanks anyway
$endgroup$
– tommycautero
Nov 27 '18 at 17:35
$begingroup$
I understand, I didn't know your background. A minor word of caution, if I may: the Lorenz system has associated a hyperbolic system with singularities, which is not really what you want, at least from your question. This corresponds to the fact that in Figure 14.10 in that book (by Hirsch, Smale and Devaney) the two parts of the graph are not onto. Without exaggeration, this makes the situation atypical from the usual one, and you may be studying a different thing from what you want to study.
$endgroup$
– John B
Nov 27 '18 at 17:54
$begingroup$
yes i know, it's not exactly what I wanted, but the chaotic nature was the main thing i was looking for, not necessary with cantor sets or symbolic dynamics. Maybe I express myself a little wrong before. Thanks a lot for the advice, have a nice day:)
$endgroup$
– tommycautero
Nov 27 '18 at 18:01
add a comment |
$begingroup$
Great starting point: projecteuclid.org/euclid.acta/1485890097
$endgroup$
– John B
Nov 27 '18 at 16:30
$begingroup$
Thank you, but this is too much difficult for me (I mean, objects used in that paper, like for example Fuchsian groups, which i have never heard about, doesn't allow me to read and understand this without before reading lot of literature concerning other field of mathematics and other definitions). I found the "strange attractor" in the Lorenz system can be what i was looking for; in Robert Devaney, Morris W. Hirsch - "Differential equations, dynamical systems, and an introduction to chaos" it seems that it's explained with basic calculus facts and without any new definition. Thanks anyway
$endgroup$
– tommycautero
Nov 27 '18 at 17:35
$begingroup$
I understand, I didn't know your background. A minor word of caution, if I may: the Lorenz system has associated a hyperbolic system with singularities, which is not really what you want, at least from your question. This corresponds to the fact that in Figure 14.10 in that book (by Hirsch, Smale and Devaney) the two parts of the graph are not onto. Without exaggeration, this makes the situation atypical from the usual one, and you may be studying a different thing from what you want to study.
$endgroup$
– John B
Nov 27 '18 at 17:54
$begingroup$
yes i know, it's not exactly what I wanted, but the chaotic nature was the main thing i was looking for, not necessary with cantor sets or symbolic dynamics. Maybe I express myself a little wrong before. Thanks a lot for the advice, have a nice day:)
$endgroup$
– tommycautero
Nov 27 '18 at 18:01
$begingroup$
Great starting point: projecteuclid.org/euclid.acta/1485890097
$endgroup$
– John B
Nov 27 '18 at 16:30
$begingroup$
Great starting point: projecteuclid.org/euclid.acta/1485890097
$endgroup$
– John B
Nov 27 '18 at 16:30
$begingroup$
Thank you, but this is too much difficult for me (I mean, objects used in that paper, like for example Fuchsian groups, which i have never heard about, doesn't allow me to read and understand this without before reading lot of literature concerning other field of mathematics and other definitions). I found the "strange attractor" in the Lorenz system can be what i was looking for; in Robert Devaney, Morris W. Hirsch - "Differential equations, dynamical systems, and an introduction to chaos" it seems that it's explained with basic calculus facts and without any new definition. Thanks anyway
$endgroup$
– tommycautero
Nov 27 '18 at 17:35
$begingroup$
Thank you, but this is too much difficult for me (I mean, objects used in that paper, like for example Fuchsian groups, which i have never heard about, doesn't allow me to read and understand this without before reading lot of literature concerning other field of mathematics and other definitions). I found the "strange attractor" in the Lorenz system can be what i was looking for; in Robert Devaney, Morris W. Hirsch - "Differential equations, dynamical systems, and an introduction to chaos" it seems that it's explained with basic calculus facts and without any new definition. Thanks anyway
$endgroup$
– tommycautero
Nov 27 '18 at 17:35
$begingroup$
I understand, I didn't know your background. A minor word of caution, if I may: the Lorenz system has associated a hyperbolic system with singularities, which is not really what you want, at least from your question. This corresponds to the fact that in Figure 14.10 in that book (by Hirsch, Smale and Devaney) the two parts of the graph are not onto. Without exaggeration, this makes the situation atypical from the usual one, and you may be studying a different thing from what you want to study.
$endgroup$
– John B
Nov 27 '18 at 17:54
$begingroup$
I understand, I didn't know your background. A minor word of caution, if I may: the Lorenz system has associated a hyperbolic system with singularities, which is not really what you want, at least from your question. This corresponds to the fact that in Figure 14.10 in that book (by Hirsch, Smale and Devaney) the two parts of the graph are not onto. Without exaggeration, this makes the situation atypical from the usual one, and you may be studying a different thing from what you want to study.
$endgroup$
– John B
Nov 27 '18 at 17:54
$begingroup$
yes i know, it's not exactly what I wanted, but the chaotic nature was the main thing i was looking for, not necessary with cantor sets or symbolic dynamics. Maybe I express myself a little wrong before. Thanks a lot for the advice, have a nice day:)
$endgroup$
– tommycautero
Nov 27 '18 at 18:01
$begingroup$
yes i know, it's not exactly what I wanted, but the chaotic nature was the main thing i was looking for, not necessary with cantor sets or symbolic dynamics. Maybe I express myself a little wrong before. Thanks a lot for the advice, have a nice day:)
$endgroup$
– tommycautero
Nov 27 '18 at 18:01
add a comment |
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$begingroup$
Great starting point: projecteuclid.org/euclid.acta/1485890097
$endgroup$
– John B
Nov 27 '18 at 16:30
$begingroup$
Thank you, but this is too much difficult for me (I mean, objects used in that paper, like for example Fuchsian groups, which i have never heard about, doesn't allow me to read and understand this without before reading lot of literature concerning other field of mathematics and other definitions). I found the "strange attractor" in the Lorenz system can be what i was looking for; in Robert Devaney, Morris W. Hirsch - "Differential equations, dynamical systems, and an introduction to chaos" it seems that it's explained with basic calculus facts and without any new definition. Thanks anyway
$endgroup$
– tommycautero
Nov 27 '18 at 17:35
$begingroup$
I understand, I didn't know your background. A minor word of caution, if I may: the Lorenz system has associated a hyperbolic system with singularities, which is not really what you want, at least from your question. This corresponds to the fact that in Figure 14.10 in that book (by Hirsch, Smale and Devaney) the two parts of the graph are not onto. Without exaggeration, this makes the situation atypical from the usual one, and you may be studying a different thing from what you want to study.
$endgroup$
– John B
Nov 27 '18 at 17:54
$begingroup$
yes i know, it's not exactly what I wanted, but the chaotic nature was the main thing i was looking for, not necessary with cantor sets or symbolic dynamics. Maybe I express myself a little wrong before. Thanks a lot for the advice, have a nice day:)
$endgroup$
– tommycautero
Nov 27 '18 at 18:01