Questions tagged [ds.dynamical-systems]
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory, topological dynamics.
2,571 questions
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Study of a dynamic system
I am interested in the following non-linear system of ODEs (all the parameters are positive):
$$
dR_{1,t}=-\lambda_1 R_{1,t}\,dt + C\,(\beta_0-\beta_1 R_{1,t} + \beta_2 \sqrt{R_{2,t}})\, dt
$$
$$
dR_{...
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Possible asymptotic behavior of recurrence function
I was wondering and tried to find what are the results known related to recurrence function of a minimal subshift $\Omega \subseteq A^{\mathbb{Z}}$, where $A$ is finite non empty subset.
If I am not ...
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Dynamics of the arithmetic–derivative family $f_k(n)=n+k(D(n)-1)$
Let $D(n)$ be the arithmetic derivative, defined by: $D(p)=1$ for primes $p$, $D(ab)=D(a)b+aD(b).$
For a fixed integer $k$, consider the dynamical system
$$f_k(n)=n+k(D(n)−1).$$
I am interested in the ...
- 1,018
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Unprovable statements and generic properties
I should start with the following disclaimer that I know virtually no logic, sorry forgive me if my questions are ill-posed. I appreciate that all of this is probably completely obvious to a logician, ...
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Can $D-D$ be a set of $2$-topological recurrence if $D$ is lacunary?
Background.
For $k \in \mathbb{N}=\{1,2,3,\dots\}$, a set $R \subseteq \mathbb{N}$ is a set of $k$-topological recurrence if for every minimal topological dynamical system $(X,T)$ and every nonempty ...
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How can one define the Lie bracket of two foliations?
In this question I am inspired by a recently closed MO question who tried to define a kind of Lie bracket on the space of 1 dimensional singular foliations.
However that idea had a gap but I think the ...
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Extreme points of a certain compact convex set
Say $\mathfrak{A}$ is a seperable $C^*$ algebra, the space $K$ of states on $\mathfrak{A}$ is compact and convex. Let $\Gamma$ be a countable discrete group acting on $\mathfrak{A}$ via $*$-hom. This ...
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Finiteness of cycles for $T_k(n):=\operatorname{rad}\bigl(\sigma^{\circ k}(n)\bigr)$ when $k$ is fixed
$\DeclareMathOperator\rad{rad}$Let $\sigma(n)=\sum_{d\mid n} d$ be the sum-of-divisors function, and let $\rad(m)=\prod_{p\mid m}p$ be the radical (with $\rad(1)=1$). For a fixed integer $k\ge 1$, ...
