A characteristic algebra for a hereditary property of identities of a fixed type τ is an algebra A such that for any variety V of type τ , we have A ∈ V if and only if every identity satisfied by V has the property p. This is equivalent to A being a generator for the variety determined by all identities of type τ which have property p. PÃlonka has produced minimal (smallest cardinality) charact...

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...