What is meant by a cubic inflection point on a circle map?
$begingroup$
I'm looking at the so-called circle map, defined by the sequence:
$$x_{n+1} = f(x_n) = f^n(x_0) = x_n+Omega - frac{k}{2pi}sin(2pi x_n) quad text{mod }1$$
where $Omega$ and $k$ are some positive parameters. It is stated in this paper1https://doi.org/10.1088/0951-7715/3/3/015 on the universality of irrational windings, that this map has a cubic inflection point. What does this mean?
1On the mode-locking universality for critical circle maps by
P. Cvitanovic, G. H. Gunaratne and M. J. Vinson,
sequences-and-series number-theory definition
edited Jan 5 at 11:50
Martin Sleziak
44.8k9118272
asked Dec 4 '18 at 1:33
genegene
38229
$endgroup$
add a comment |
$begingroup$
I'm looking at the so-called circle map, defined by the sequence:
$$x_{n+1} = f(x_n) = f^n(x_0) = x_n+Omega - frac{k}{2pi}sin(2pi x_n) quad text{mod }1$$
where $Omega$ and $k$ are some positive parameters. It is stated in this paper1https://doi.org/10.1088/0951-7715/3/3/015 on the universality of irrational windings, that this map has a cubic inflection point. What does this mean?
1On the mode-locking universality for critical circle maps by
P. Cvitanovic, G. H. Gunaratne and M. J. Vinson,
sequences-and-series number-theory definition
edited Jan 5 at 11:50
Martin Sleziak
44.8k9118272
asked Dec 4 '18 at 1:33
genegene
38229
$endgroup$
add a comment |
$begingroup$
I'm looking at the so-called circle map, defined by the sequence:
$$x_{n+1} = f(x_n) = f^n(x_0) = x_n+Omega - frac{k}{2pi}sin(2pi x_n) quad text{mod }1$$
where $Omega$ and $k$ are some positive parameters. It is stated in this paper1https://doi.org/10.1088/0951-7715/3/3/015 on the universality of irrational windings, that this map has a cubic inflection point. What does this mean?
1On the mode-locking universality for critical circle maps by
P. Cvitanovic, G. H. Gunaratne and M. J. Vinson,
sequences-and-series number-theory definition
edited Jan 5 at 11:50
Martin Sleziak
44.8k9118272
asked Dec 4 '18 at 1:33
genegene
38229
$endgroup$
I'm looking at the so-called circle map, defined by the sequence:
$$x_{n+1} = f(x_n) = f^n(x_0) = x_n+Omega - frac{k}{2pi}sin(2pi x_n) quad text{mod }1$$
where $Omega$ and $k$ are some positive parameters. It is stated in this paper1https://doi.org/10.1088/0951-7715/3/3/015 on the universality of irrational windings, that this map has a cubic inflection point. What does this mean?
1On the mode-locking universality for critical circle maps by
P. Cvitanovic, G. H. Gunaratne and M. J. Vinson,
sequences-and-series number-theory definition
sequences-and-series number-theory definition
edited Jan 5 at 11:50
Martin Sleziak
44.8k9118272
asked Dec 4 '18 at 1:33
genegene
38229
edited Jan 5 at 11:50
Martin Sleziak
44.8k9118272
asked Dec 4 '18 at 1:33
genegene
38229
edited Jan 5 at 11:50
Martin Sleziak
44.8k9118272
edited Jan 5 at 11:50
Martin Sleziak
44.8k9118272
edited Jan 5 at 11:50
Martin Sleziak
44.8k9118272
44.8k9118272
asked Dec 4 '18 at 1:33
genegene
38229
asked Dec 4 '18 at 1:33
genegene
38229
asked Dec 4 '18 at 1:33
genegene
38229
38229
add a comment |
add a comment |
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