On stronger forms of sensitivity in non-autonomous systems
In this paper, some stronger forms of transitivity are discussed for non-autonomous discrete dynamical systems (NDS). The following is the main result: Theorem. Let \((X,f_{1,\infty})\) be an NDS generated by a family \(f_{1,\infty}\) of feeble open maps commuting with \(f\) and fulfilling \(\sum_i D(f_i,f)< \infty\). Then i) \((X,f)\) is syndetically transitive iff \((X,f_{1,\infty})\) is syndetically transitive ii) \((X,f)\) is topologically ergodic iff \((X,f_{1,\infty})\) is topologically ergodic iii) \((X,f)\) is syndetically sensitive iff \((X,f_{1,\infty})\) is syndetically sensitive iv) \((X,f)\) is thickly sensitive iff \((X,f_{1,\infty})\) is thickly sensitive v) \((X,f)\) is thickly syndetic sensitive iff \((X,f_{1,\infty})\) is thickly syndetic sensitive vi) \((X,f)\) is ergodically sensitive iff \((X,f_{1,\infty})\) is ergodically sensitive vii) \((X,f)\) is multi-sensitive iff \((X,f_{1,\infty})\) is multi-sensitive. Further aspects occasioned by these developments are also discussed.
scientific article; zbMATH DE number 6965413