What is meant by a cubic inflection point on a circle map?












1












$begingroup$


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







share|cite|improve this question











$endgroup$

















    1












    $begingroup$


    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







    share|cite|improve this question











    $endgroup$















      1












      1








      1





      $begingroup$


      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







      share|cite|improve this question











      $endgroup$




      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






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 5 at 11:50









      Martin Sleziak

      44.7k9117272




      44.7k9117272










      asked Dec 4 '18 at 1:33









      genegene

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