Examples of semigroup

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We give a necessary and sufficient condition for a semigroup to be hypercyclic.
It is easy to see that this map is an isomorphism of dynamical systems, and hence a semigroup isomorphism.
Now we obtain the sufficient and necessary condition to be semi-hyperbolic for a finitely generated rational semigroup.
Furthermore, any intermediate value on the curve may be taken as initial condition due to the semigroup property of the flow.
We also study the semigroup and the toric ideal associated with semi-graphoids.
It is a semigroup with the semigroup operation being a composition of maps.
This is in order to prove our main result in the case when is a semigroup.
This defines an 'action' of the semigroup on every dynamical system.
The heat semigroup is only one example, but may be of particular interest.
The case of unbounded infinitesimal generators makes the linear semigroup formulation of chaos applicable to linear partial differential equations.
The dual statements hold for pointed homomorphisms and semigroup homomorphisms.
We consider actions of the free semigroup with two generators on the real line, where the generators act as affine maps, one contracting and one expanding, with distinct fixed points.
A semigroup associated with a transformation group.
We give necessary and sufficient conditions on the semigroup to be hypercyclic, and sufficient conditions on the spectrum of an operator to generate a hypercyclic semigroup.
A semigroup associated with the k -bonacci numbers with dynamic interpretation.
W e close this section with some necessary conditions on the dual semigroup.

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