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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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        Foliations with algebraic foliation chart

        An algebraic foliation chart for a foliated manifold is a foliation chart for which the transition maps are polynomial maps. What is an example of an analytic foliation of the Euclidean space $\...
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        132 views

        Reading list in dynamical systems

        So I’ve managed to gather from various sources, a plethora of books in dynamical systems. Now I’m wondering which of them to read, and in what order. So far these are the books I’ve found/been ...
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        What are the applications of topological quantum field theory to continuous-time dynamical systems?

        From wikipedia: In dynamics, all continuous time dynamical systems, with and without noise, are Witten-type TQFTs and the phenomenon of the spontaneous breakdown of the corresponding topological ...
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        286 views

        Growing a chain of unit-area triangles: Fills the plane?

        Define a process to start with a unit-area equilateral triangle, and at each step glue on another unit-area triangle.                     $50$ ...
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        153 views

        Why do unstable manifolds of two close point intersect each other in Baker map?

        Let $M$ be $S^1 \times [-1,1]$, $f$ a baker map on $M$ and for $p, q \in M$ consider $W^s_p$ the stable manifold in $p$ (i.e. the set of points whose forward orbit tend to the forward orbit of $p$) ...
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        A sufficient condition for uniform convergence of ergodic averages?

        Given a measure preserving system $(X, mu, T)$ where $\mu(X) = 1$, we say $T$ is uniformly weak mixing if for all measurable $A$, $B$ and every $\varepsilon > 0$, there exists some $N$ independent ...
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        Does an asymptotic component with large size in a minimal subshift always exist?

        Let $(X, T)$ be a minimal subshift, i.e. $X$ is a closed $T$-invariant subset of $A^\mathbb{Z}$, where $T$ is the shift. A pair $x,y\in X$ is asymptotic if $d(T^nx, T^ny)$ goes to zero as $n\to\infty$....
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        A bisector line bundle over the total space of a principal bundle

        Let $(P,X,G)$ be a principal bundle where $G$ is a Lie group which acts on $P$. We fix a principal connection on $P$ and a right invariant metric for $G$. These structures define a unique Riemannian ...
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        Example of a “very noisy” SDE on a compact manifold with zero maximal Lyapunov exponent

        Setting: Let $M$ be a compact connected $C^\infty$ Riemannian manifold of dimension $D \geq 2$, with $\lambda$ the normalised Riemannian volume measure. Write $T_{\neq 0}M \subset TM$ for the non-...
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        Topological entropy of logistic map $f(x) = \mu x (1-x)$, $f:[0,1] \to [0,1]$ for $\mu \in (1,3)$

        As stated in the question, I want to find the topological entropy of the logistic map on the interval $[0,1]$ for a "nice" range of the parameter $\mu$, namely $\mu \in (1,3)$. I think the fact that $...
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        Lyapunov functions for determining the stability of invariant sets?

        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(...
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        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. ...
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        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 ...
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        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 \...
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        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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        山西福彩快乐十分钟
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