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For dynamical systems with the shadowing property, we provide a method of approximation of invariant measures by ergodic measures supported on odometers and their almost 1-1 extensions.
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M. Kuchta, Shadowing property of continuous maps with zero topological entropy . Proc. Amer. Math. Soc. 119
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D. Richeson and J. Wiseman, Chain recurrence rates and topological entropy , Topology Appl. 156
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T.K.S. Moothathu, Implications of pseudo-orbit tracing property for continuous maps on compacta , Top. Appl. 158
2011
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J. Li, P. Oprocha, Shadowing property, weak mixing and regular recurrence , J. Dynam. Differential Equations, 25
2013
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T.K.S. Moothathu, and P. Oprocha, Shadowing, entropy and minimal subsystems , Monatsh. Math. 172
2013
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G. Harańczyk, D. Kwietniak, P. Oprocha, Topological structure and entropy of mixing graph maps. Ergodic Theory Dynam. Systems 34
2014
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D. Kwietniak, M. Łacka, P. Oprocha, A panorama of specification-like properties and their consequences , Dynamics and Numbers, Contemporary Mathematics, vol. 669, 2016, pp. 155–186
2016
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