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Jul
3
comment does an exponential bound on a Lyapunov candidate implies asymptotic stability?
en.wikipedia.org/wiki/Krasovskii%E2%80%93LaSalle_principle
Jul
3
answered stability of equilibria for $n$-dimensional nonlinear systems of differential equations: examples
Jun
13
answered Why do mathematicians use $\Delta$ instead of $\nabla^2$?
Jun
12
comment Stuck while trying to simplifying this PDE identity
@RobertLewis Yup!
Jun
12
comment Stuck while trying to simplifying this PDE identity
@RobertLewis From what I can tell, $u$ is a vector-valued function, so $\nabla u$ is a matrix.
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".