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Questions tagged [ds.dynamical-systems]

Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.

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Suppose we have a dynamical system $\dot{x}=f(x)$ with an equillibrium $x_0$. It is known that $x_0$ is Lyapunov stable in this sense if there exists $V:\mathbb{R}^n\rightarrow\mathbb{R}$ such that V(... 0answers 46 views Can a nonlinear dynamical system be rewritten in terms of constraints? My question is based on thoughts after reading to a specific section in the paper "On Contraction Analysis for Nonlinear Systems" by W. Lohmiller and JJ. Slotine, Section 4.2 Constrained Systems. ... 0answers 43 views conditions for asymptotic comparison to hold I have the following simple dynamical system: \begin{align} x_1' &= a - f(x_2)x_1\\ x_2' &= bx_1 - cx_2, \end{align} where all parameters and initial conditions are positive.f(x_2)$is a ... 0answers 41 views Equidistribution of linear forms over euclidean ball Given a vector$v\in \mathbb{Z}^d\setminus\{0\}$, an irrational number$\eta$and some big$M>0$what type of bound can one get on$$\sum_{w\in \mathbb{Z}^d\cap B(0, M)}\exp(2\pi i \eta \cdot \... 0answers 24 views Phase space of double pendulum [migrated] Let$M$be the phase space of a double pendulum system. What is known about the manifold$M\$? Do we know it's homotopy typed? Do we know its (co)homology? Are there any references tackling these ...

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