This is redundant, potentially confusing, and pretentious.
Mathematics has a very well-established subject classification.
It was last revised in 2020 but has been around for decades.
MSC page on zbMATH
MSC page on AMS
For ##a = 0.1## you have a complex conjugate pair of eigenvalues, so they have the same magnitude, and the system is not stiff. I would think that pretty much any reasonable numerical method would be able to approximate the solution on a large time interval.
Also, I assume you are aware that...
Is ##a## a parameter? If so, then the system you provide is planar, autonomous, and linear. You could easily solve it by hand. In what sense do you think it is chaotic?
If you insist on solving it numerically, my hint would be to look at the pair of eigenvalues and their relative magnitude, as...
You wrote that
So, why are you interested in this question? Is your interest somehow "academic"?
In short: Using pirated copies of closed-source software is a recipe for disaster.
Disabling or postponing updates on an official copy of software, closed or open, is a recipe for unhappiness. See...
Maybe try to actually run it through Maple with reference to post #6.
It is a triviality, nothing else. And it certainly does not have anything to do with branches of square roots.
One must be careful with such overly general statements. See, for example, Linear Chaos by Erdmann and Manguillot.
Your remark fits well into the context of ergodic theory. (Also see the book mentioned above.)
That is regrettable. I think MHB was a very good forum for its target audience, with high quality facilities for mathematical writing and effective non-intrusive moderation. I would rather have seen MHB exist separately alongside PF.
Thank you for your response, it is appreciated. I also appreciate it that you yourself are, indeed, not anonymous.
My main reason for being surprised and irritated by the ongoing thread about the war in Ukraine is that since long before the start of that war, I came to agree with the OP in this...
There are certain words that I write with a capital mid-sentence, but they do not appear in the above quote.
In any case, indeed, I have no interest in opening any can and risk having it thrown in my face in an online discussion with mostly anonymous parties.