## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
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- Electronic Research Announcements
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- AIMS Mathematics

DCDS

Let $\varphi(t,\cdot,u)$ be the flow of a control system on a
Riemannian manifold $M$ of constant curvature. For a given initial
orthonormal frame $k$ in the tangent space $T_{x_{0}}M$ for some
$x_{0}\in M$, there exists a unique decomposition
$\varphi_{t}=\Theta_{t}\circ\rho_{t}$ where $\Theta_{t}$ is a
control flow in the group of isometries of $M$ and the remainder
component $\rho_{t}$ fixes $x_{0}$ with derivative
$D\rho_{t}(k)=k\cdot s_{t}$ where $s_{t}$ are upper triangular
matrices. Moreover, if $M$ is flat, an affine component can be
extracted from the remainder.

CPAA

Hyperbolic affine-linear flows on vector bundles possess unique bounded
solutions on the real line. Hence they are topologically skew conjugate to
their linear parts. This is used to show a classification of inhomogeneous
bilinear control systems.

DCDS

Algebraic semigroups describing the dynamic behavior are associated to
compact, locally maximal chain transitive subsets. The construction is based
on perturbations and associated local control sets. The dependence on the
perturbation structure is analyzed.

DCDS

For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset *Q* of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure. The main results show that this entropy is invariant under measurable transformations and that it is already determined by certain subsets of *Q* which are characterized by controllability properties.

keywords:
Invariance entropy
,
quasi-stationary measures
,
control sets
,
coder-controllers
,
transitivity set

## Year of publication

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