2015年9月18日 · $\begingroup$ Note that this is the immediate basin of attraction, not the full basin of attraction: there are also points not in $(-1,+\infty)$ which are attracted to the attracting fixed point. $\endgroup$ –

2016年4月23日 · My text mentioned nothing about the basin of attraction being an open set-Of course this could imply that the audience is meant to think on a deeper level about the said properties of it being an open set. It is in a given example that I concluded that the author implicitly claimed that the basin of attraction is an open set.

2015年11月6日 · Tour Start here for a quick overview of the site

2021年6月20日 · Thanks a lot ! Is it also possible to divide the xyz space into two regions, where one region is the basin of attraction of the stable restpoint (1,0,0) and the second region is the basin of attraction of the stable restpoint (0,0,0)? $\endgroup$ –

2015年1月19日 · $\begingroup$ I'm sorry for beeing so blunt. My question is off course how one would prove this. In the examples I've seen so far they usually prove that a fixed point has a certain basin of attraction by proving that the function is decreasing or increasing for certain values within the basin of attraction.

2016年11月30日 · I want to prove that the immediate basin of attraction of a finite attracting fixed or periodic point is simply connected. We are talking about complex numbers ! According to Remark 2 p. 281 and Exercise 4.2 p. 283 of the text of Devaney [ 1 ],

2020年7月4日 · Basin of attraction of the Lorenz attractor. Ask Question Asked 4 years, 6 months ago. Modified 1 year, 8 ...

2020年8月19日 · Years and years ago, back when I first became interested in fractals [but didn't know much about anything], I vaguely remember coming across an interesting theorem. The gist of it was that "every basin of attraction contains at least one critical point". Am I remembering this correctly? Does anybody know any details about it?

2018年8月18日 · $\begingroup$ @Moo Yes! seems like (0.63,0.63) is not in the basin of attraction. So now my posted question makes sense. My question, in short, is why the reduced ODE cannot predict the basin of attraction. $\endgroup$ –

2024年3月15日 · I am trying to construct basins of attraction using the newton's method for the system of two equations whose roots are real. I need to develop a code to get basin of attraction. Unfortunately, my...