‎Let $(Sigma_P,sigma_P)$ be the space of a spacing shifts where $Psubset mathbb{N}_0=mathbb{N}cup{0}$ and $Sigma_P={sin{0,1}^{mathbb{N}_0}: ‎s_i=s_j=1 mbox{ if } |i-j|in P cup{0}}$ and $sigma_P$ the shift map‎. ‎We will show that $Sigma_P$ is mixing if and only if it has almost specification property with at least two periodic points‎. ‎Moreover‎, ‎we show that if $h(sigma_P)=0$‎, ‎then $Sigma_...

We study the Bowen topological entropy of generic and irregular points for certain dynamical systems. define noncompact sets flows, analogous to Bowen's definition. show that this coincides with time-1 map on any set. also a inequality flows; namely, metric respect every invariant measure continuous flow is an upper bound set same measure, equality always true if ergodic. propose definition alm...

Shift spaces with the specification property are intrinsically ergodic, i.e. they have a unique measure of maximal entropy. This can fail for shifts with the weaker almost specification property. We define a new property called one-sided almost specification, which lies in between specification and almost specification, and prove that it guarantees intrinsic ergodicity if the corresponding mist...