Chaos

1. List of fractals by Hausdorff dimension—Wikipedia (2019). https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension. Accessed 31 Jul 2019

2. Alligood, K., Sauer, T., Yorke, J.: Chaos: An Introduction to Dynamical Systems. Textbooks in Mathematical Sciences. Springer, New York (2000)

   Google Scholar 

3. Banks, J., Brooks, J., Cairns, G., Davis, G., Stacey, P.: On Devaney’s Definition of Chaos. Amer. Math. Monthly 99, 332–334 (1992). https://doi.org/10.2307/2324899

   Article  Google Scholar 

4. Beck, C., Schögl, F.: Thermodynamics of Chaotic Systems: An Introduction. Cambridge Nonlinear Science Series. Cambridge University Press, Cambridge (1993). https://doi.org/10.1017/CBO9780511524585

   Book  Google Scholar 

5. Cvitanović, P., Artuso, R., Mainieri, R., Tanner, G., Vattay, G.: Lyapunov exponents. In: Chaos: Classical and Quantum, chap. 6. Niels Bohr Institute, Copenhagen (2012). http://ChaosBook.org/version14ChaosBook.org/version14

6. Eckmann, J.P., Procaccia, I.: Fluctuations of dynamical scaling indices in nonlinear systems. Phys. Rev. A 34, 659–661 (1986). https://doi.org/10.1103/PhysRevA.34.659

   Article  Google Scholar 

7. Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349 (1983)

   Article  Google Scholar 

8. Grassberger, P., Procaccia, I.: Estimation of the Kolmogorov entropy from a chaotic signal. Phys. Rev. A 28, 2591–2593 (1983). https://doi.org/10.1103/PhysRevA.28.2591

   Article  Google Scholar 

9. Grassberger, P., Procaccia, I.: Measuring the strangeness of strange attractors. Phys. D 9, 189–208 (1983)

   Article  Google Scholar 

10. Halsey, T.C., Jensen, M.H., Kadanoff, L.P., Procaccia, I., Shraiman, B.I.: Fractal measures and their singularities: the characterization of strange sets. Phys. Rev. A 33, 1141–1151 (1986). https://doi.org/10.1103/PhysRevA.33.1141

    Article  Google Scholar 

11. Horita, T., Hata, H., Mori, H., Morita, T., Tomita, K.: Singular local structures of chaotic attractors due to collisions with unstable periodic orbits in two-dimensional maps. Progr. Theor. Phys. 80(6), 923–928 (1988). https://doi.org/10.1143/PTP.80.923

    Article  Google Scholar 

12. Jayawardena, A., Xu, P., Li, W.K.: Modified correlation entropy estimation for a noisy chaotic time series. Chaos 20(2), 023104 (2010)

    Article  Google Scholar 

13. Li, T.Y., Yorke, J.A.: Period three implies chaos. Am. Math. Mon. 82(10), 985–992 (1975)

    Article  Google Scholar 

14. Lorenz, H.W.: Nonlinear Dynamical Economics and Chaotic Motion, 2nd edn. edn. Springer, Berlin (1993)

    Google Scholar 

15. Oono, Y., Takahashi, Y.: Chaos, external noise and fredholm theory. Progr. Theor. Phys. 63(5), 1804–1807 (1980). https://doi.org/10.1143/PTP.63.1804

    Article  Google Scholar 

16. Ott, E.: Attractor dimensions. Scholarpedia 3(3), 2110 (2008). https://doi.org/10.4249/scholarpedia.2110. Revision #91015

17. Peinke, J., Parisi, J., Rössler, O.E., Stoop, R.: Encounter with Chaos: Self-Organized Hierarchical Complexity in Semiconductor Experiments. Springer, Berlin (2012)

    Google Scholar 

18. Pesin, Y.B.: Characteristic Lyapunov exponents and smooth ergodic theory. Russ. Math. Surv. 32, 55–114 (1977). https://doi.org/10.1070/RM1977v032n04ABEH001639

    Article  Google Scholar 

19. Robinson, J.C.: Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

20. Sano, M., Sato, S., Sawada, Y.: Global spectral characterization of chaotic dynamics. Progr. Theor. Phys. 76(4), 945–948 (1986). https://doi.org/10.1143/PTP.76.945

    Article  Google Scholar 

21. Sivakumar, B., Berndtsson, R.: Advances in Data-Based Approaches for Hydrologic Modeling and Forecasting, chap. 9, pp. 411–461. World Scientific, Singapore (2010)

    Google Scholar 

22. Stoop, R.: Dependence of phase transitions on small changes. Phys. Rev. E 47, 3927–3931 (1993). https://doi.org/10.1103/PhysRevE.47.3927

    Article  Google Scholar 

23. Stoop, R.: On hyberbolic elements hiding phase transitions. Phys. Lett. A 173(4), 369–372 (1993). https://doi.org/10.1016/0375-9601(93)90252-U

    Article  Google Scholar 

24. Stoop, R.: Bivariate thermodynamic formalism and anomalous diffusion. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 49(6), 4913–4918 (1994). https://doi.org/10.1103/physreve.49.4913

    Google Scholar 

25. Stoop, R.: The diffusion-related entropy function: the enhanced case. Europhys. Lett. 29(6), 433–438 (1995). https://doi.org/10.1209/0295-5075/29/6/001

    Article  Google Scholar 

26. Stoop, R.: Thermodynamic approach to deterministic diffusion of mixed enhanced-dispersive type. Phys. Rev. E 52, 2216–2219 (1995). https://doi.org/10.1103/PhysRevE.52.2216

    Article  Google Scholar 

27. Stoop, R., Gomez, F.: Auditory power-law activation avalanches exhibit a fundamental computational ground state. Phys. Rev. Lett. 117, 038102 (2016). https://doi.org/10.1103/PhysRevLett.117.038102

    Article  Google Scholar 

28. Stoop, R., Peinke, J., Parisi, J., Röhricht, B., Huebener, R.: A p-Ge semiconductor experiment showing chaos and hyperchaos. Phys. D: Nonlinear Phenom. 35(3), 425–435 (1989)

    Article  Google Scholar 

29. Szépfalusy, P., Tél, T.: New approach to the problem of chaotic repellers. Phys. Rev. A 34, 2520–2523 (1986). https://doi.org/10.1103/PhysRevA.34.2520

    Article  Google Scholar 

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Authors and Affiliations

1. University of Bari, Department of Economics and Finance, Bari, Italy

   Giuseppe Orlando & Giovanni Taglialatela

2. University of Camerino, School of Sciences and Technology, Camerino, Italy

   Giuseppe Orlando

3. Institute of Neuroinformatics, ETHZ/University of Zürich, Zurich, Switzerland

   Ruedi Stoop

Corresponding author

Correspondence to Giuseppe Orlando .

Editors and Affiliations

1. Department of Economics & Finance, University of Bari Aldo Moro, Bari, Italy

   Giuseppe Orlando

2. Technical University of Madrid Center for Biomedical Technology, Campus Montegancedo, Pozuelo de Alarcón, Madrid, Spain

   Alexander N. Pisarchik

3. Institute of Neuroinformatics, Swiss Federal Institute of Technology, Zürich, Switzerland

   Ruedi Stoop