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 Yearling
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Apr
4
comment System of first order ODEs with coherent sinusoidal time varying coefficient
@Artem: In practise, the monodromy matrix is found numerically. I don't see what is wrong in what I said. That is the best you can do in general case.
Apr
2
comment System of first order ODEs with coherent sinusoidal time varying coefficient
Floquet theory gives you everything you need here. Using that, you can convert the system into a autonomous system, and then, just look at eigenvalues to determine stability. I don't know what else you want from a more 'powerful theory' ?
Apr
1
comment System of first order ODEs with coherent sinusoidal time varying coefficient
This is covered under Floquet theory. $B(t)=A_0+A_1cos(\omega t)$ is a periodic matrix with period $2\pi/\omega$. en.wikipedia.org/wiki/Floquet_theory
Jan
24
awarded  Yearling
Dec
8
awarded  Caucus
Sep
24
awarded  Autobiographer
Aug
1
comment Link between the two definitions of a “hyperbolic point”
In both cases, this means there exist directions in which perturbations don't grow in the linearized system.
Jul
3
comment Does a pseudo-Anosov homeomorphism of a punctured surface possess infinitely many periodic points?
It certainly does for disc with finite number of punctures. people.clas.ufl.edu/boyland/files/stir.pdf
Jul
2
awarded  Curious
Jun
2
comment Estimating a dynamical system's behavior without using Liapunov theorem
Solve for z explicitly as function of time. After you substitute for z in first two equations, it becomes a linear 2nd order system which has analytical solution (e.g. via Laplace transform )
May
30
comment Does Hyperbolic + Not Asymptotically Linearly Stable imply Not Asymptotically Stable?
Answer is Yes by Hartman Grobman.
May
27
comment Non-integrable systems
KAM theorem tells us how the nice properties of integrable systems are (or are not) preserved as you add a bit of perturbation.
May
20
comment iterates of generalized matrix system
I don't see how this is close to linear if Q is a general function. Seems to me that the representation is very general.
Apr
30
comment Free Vibrations - Simple Harmonic Motion
Do you know how to write equations of motion of this system?
Apr
23
comment Physical interpretation of Ergodicity.
@Did: Indeed. I guess a better way to put it to motivate physical interpretation would be that "the neighborhood of each point is visited the same number of times".
Apr
22
comment Transient Behaviour Transient Property Lorenz Equation
He is interested in long term behavior of the system. So the best guess here is that he is referring to transient part of trajectory which occurs before settling down to : fixed point, periodic or quasiperiodic orbit.
Apr
22
comment Physical interpretation of Ergodicity.
Your guess is correct. Ergodicity (with respect to some measure, here we take arc length) can be heuristically understood as time average=space average. What it means is that if you divide the circle into N bins of varying sizes, and start your dynamical system in one of the bins, the time spent in each of bins will be proportional to the area of that bin. In the limit of each bin size going to 0, you get the result that each point is visited the same number of times.
Apr
21
comment Marginal stability and centers of nonlinear dynamical systems
center manifold theory is what you want to look into.
Apr
18
comment Recommend resources on dynamical systems and singularities
Try Kuznetsov's Applied bifurcation theory book. Also, Hale and Kocak's dynamics and bifurcations.
Apr
2
answered Reference about the Conley index thoery