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Results tagged with ds.dynamical-systems
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user 51484
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
11
votes
1
answer
1k
views
How to eliminate secular terms for perturbed non-oscillatory equations?
Even in a linear second order equation like $x''+x'+\epsilon x=0$ the standard asymptotic expansion has a secular term already in the first order of $\epsilon$, namely
$$x(t)=a_0+b_0e^{-t}+\epsilon(a …
- 1,731
10
votes
0
answers
222
views
Rigorous results on chaos in a driven damped pendulum
The harmonically driven damped pendulum is often used as a simple example of a chaotic system, the equation is just $\ddot{\phi}+\frac1q\dot{\phi}+\sin\phi=A\cos(\omega t)$. As long as $A$ and $\omega …
- 1,731
7
votes
0
answers
442
views
Geometric bang-bang theorem for nonlinear optimal control
The classical bang-bang theorem is usually stated for linear systems (e.g. Control Theory from the Geometric Viewpoint by Agrachev-Sachkov, p. 209). Sussman proved a nice generalization for systems af …
- 1,731