Phenom

Hi Hil, Sorry, I jumbled up the numbers while typing. The saddle fixed point is (-1.53333,-1.53333) for R = -0.3, S =-0.1, b = 0.5401. Even then I got the plot in actual coding but not in MATCONTM (it says no convergence/ norm but kind of plots the stable manifold)? do you have any thoughts why this is happening? Please find the attached plots. Thanks, Phenom

Hi Hil, Sorry, I jumbled up the numbers while typing. The saddle fixed point is (-1.53333,-1.53333) for R = -0.3, S =-0.1, b = 0.5401. Even then I got the plot in actual coding but not in MATCONTM (it says no convergence error but kind of plots the stable manifold)? do you have any thoughts why this is happening? Please find the attached plots. Thanks, Sishu

Thanks Hil. I was trying the following map x' = y y' = ((-S(b+1))^3 + R(b+1)^2)/(R^3) - bx - y^2 +Rxy + S(y^3) with parameters R = -0.3, S = -0.1, b = 0.5401 with saddle fixed point (-5.1336,-5.1336). Trying manually by coding, I can obtain the stable and unstable manifolds of the saddle point. But trying it in Matcontm: I am not able to compute the unstable manifold (it says no ocnvergence), the stable manifold is computed. Below are some snapshots. I am not sure why?

Sorry for that! Suppose I am continuing homoclinic tangency in the Henon map. I got the tangency curve in two parameters. Now I took a point on the tangency curve and checked whether I am getting a tangnecy or not. I do get tangency! (a single tangential intersection between the stable and unstable manifolds would imply infinitely many tangencies) but as I move closer to the fixed point, I observe that there is still a small gap between the manifolds (the more we go near to fixed point, the gap increases)...

Oh thanks!. Is there any variable which controls the tolerance of |a - (b+3)| or if it was a more complicated equation? I want to make the tolerance as less as 10^-11. Thanks!

Oh thanks!. Is there any variable which controls the tolerance of |a - (b+3)| or if it was a more complicated equation? I want to make the tolerance as less as 10^-11. Thanks, Sishu

Suppose we consider the Henon map x' = 1 - ax^2 + y y' = b x a,b are parameters. While entering this map into matcontm, I tried to give the saddle fixed point values and suppose we have a condition on the parameters as a = b + 3 (at which i obtain saddle fixed points) , so I was thinking of giving a single value of b and then it could automatically calculate the value of a. While calculating the invariant manifolds, it gives me an error in MATLAB saying "Error while evaluating UIControl Callback"...