What is topological about topological dynamics?

Chris Good; Sergio Macías

doi:10.3934/dcds.2018043

journal article Jan 01, 2018

What is topological about topological dynamics?

Discrete and Continuous Dynamical Systems Vol. 38 No. 3 pp. 1007-1031 · American Institute of Mathematical Sciences (AIMS)

View at Publisher Save 10.3934/dcds.2018043

Topics

No keywords indexed for this article. Browse by subject →

References

41

[1]

E. Akin, The General Topology of Dynamical Systems, Graduate Studies in Mathematics (1), Amer. Math. Soc., Providence, RI, 1993.

[2]

E. Akin, J. Auslander and K. Berg, When is a transitive map chaotic?, in Convergence in Ergodic Theory and Probability, (Columbus, OH, 1993), Ohio State Univ. Math. Res. Inst. Publ., de Gruyter, Berlin, 5 (1996), 25-40. 10.1515/9783110889383.25

[3]

10.4064/sm8553-7-2016

[4]

10.1016/j.topol.2012.04.016

[5]

10.2140/pjm.2017.291.1

[6]

N. Aoki, Topological dynamics, in K. Morita and J. Nagata, Topics in General Topology, North Holland, Amsterdam, New York, Oxford, Tokyo, 41 (1989), 625-740. 10.1016/s0924-6509(08)70161-2

[7]

N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems, North Holland, Amsterdam, London, New York, Tokyo, 1994.

[8]

10.1090/s0002-9939-2014-12034-x

[9]

[10]

[11]

10.2307/2324899

[12]

A. D. Barwell, ω-Limit Sets of Discrete Dynamical Systems, Ph. D. Dissertation, The University of Birmingham, 2010.

[13]

10.4064/fm219-3-2

[14]

[15]

10.1016/j.aim.2012.05.024

[16]

10.1007/s11253-014-0860-8

[17]

W. R. Brian, Abstract omega-limit sets, preprint, Available from: <a href="https://wrbrian.files.wordpress.com/2012/01/omegalimitsets.pdf" target="_blank">https://wrbrian.files.wordpress.com/2012/01/omegalimitsets.pdf</a>.

[18]

10.1090/s0002-9939-1960-0113210-2

[19]

10.2140/pjm.1960.10.1163

[20]

10.1007/s10883-013-9182-7

[21]

[22]

R. Engelking, General Topology, Sigma series in pure mathematics, Vol. 6, Heldermann, Berlin, 1989.

[23]

10.4064/fm136-2-2016

[24]

10.1088/0951-7715/6/6/014

[25]

[26]

Analogues of Auslander–Yorke theorems for multi-sensitivity

Wen Huang, SERGIĬ KOLYADA, Guohua Zhang

Ergodic Theory and Dynamical Systems 10.1017/etds.2016.48

[27]

10.1007/s11766-005-0032-6

[28]

10.1090/s0002-9939-1964-0159307-6

[29]

10.1090/s0002-9947-1977-0428315-3

[30]

10.4064/fm-34-1-127-143

[31]

10.1090/s0002-9947-1951-0042109-4

[32]

[33]

10.1016/0166-8641(82)90040-2

[34]

10.1017/s0305004100031406

[35]

S. Ruette, Chaos on the Interval, University Lecture Series, 67. American Mathematical Society, Providence, RI, 2017. 10.1090/ulect/067

[36]

On Maps with Dense Orbits and the Definition of Chaos

Stephen Silverman

Rocky Mountain Journal of Mathematics 10.1216/rmjm/1181072815

[37]

10.2307/2975629

[38]

10.1007/s10114-016-5050-1

[39]

10.1016/j.chaos.2008.07.014

[40]

S. Willard, General Topology, Addison-Wesley, Reading, Massachusetts; London, 1970.

[41]

10.1016/j.topol.2016.07.016

Cited By

31

Sensitivity, Devaney’s chaos and Li–Yorke $$\varepsilon $$-chaos

Huoyun Wang, Qing Liu · 2020

Semigroup Forum

Metrics

31

Citations

41

References

Details

Published: Jan 01, 2018
Vol/Issue: 38(3)
Pages: 1007-1031

Authors

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D. F., C. P. 04510. México

Cite This Article

Chris Good, Sergio Macías (2018). What is topological about topological dynamics?. Discrete and Continuous Dynamical Systems, 38(3), 1007-1031. https://doi.org/10.3934/dcds.2018043

What is topological about topological dynamics?

You May Also Like