# American Institute of Mathematical Sciences

January  2019, 39(1): 1-18. doi: 10.3934/dcds.2019001

## Markov-Dyck shifts, neutral periodic points and topological conjugacy

 1 Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany 2 Department of Mathematics, Joetsu University of Education, Joetsu 943 - 8512, Japan

Received  May 2017 Revised  June 2018 Published  October 2018

We study the neutral periodic points of Markov-Dyck shifts of finite strongly connected directed graphs. Under certain hypothesis on the structure of the graphs $G$ we show, that the topological conjugacy of their Markov-Dyck shifts implies the isomorphism of the graphs.

Citation: Wolfgang Krieger, Kengo Matsumoto. Markov-Dyck shifts, neutral periodic points and topological conjugacy. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 1-18. doi: 10.3934/dcds.2019001
##### References:

show all references

##### References:
$G(1, 0, 2, 0, \dots)$
$G(1, (1, 0, 3, 0, \dots))$
$G_{2, 3}(4.1)$
$G_{3.2}(4.1)$
 [1] Kengo Matsumoto. On the Markov-Dyck shifts of vertex type. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 403-422. doi: 10.3934/dcds.2016.36.403 [2] Eric Babson and Dmitry N. Kozlov. Topological obstructions to graph colorings. Electronic Research Announcements, 2003, 9: 61-68. [3] Marian Gidea, Yitzchak Shmalo. Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics. Discrete & Continuous Dynamical Systems - A, 2018, 38 (12) : 6123-6148. doi: 10.3934/dcds.2018264 [4] Mario Roy, Mariusz Urbański. Random graph directed Markov systems. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 261-298. doi: 10.3934/dcds.2011.30.261 [5] Adriano Da Silva, Alexandre J. Santana, Simão N. Stelmastchuk. Topological conjugacy of linear systems on Lie groups. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3411-3421. doi: 10.3934/dcds.2017144 [6] Steven T. Piantadosi. Symbolic dynamics on free groups. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 725-738. doi: 10.3934/dcds.2008.20.725 [7] Mario Roy, Mariusz Urbański. Multifractal analysis for conformal graph directed Markov systems. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 627-650. doi: 10.3934/dcds.2009.25.627 [8] James Kingsbery, Alex Levin, Anatoly Preygel, Cesar E. Silva. Dynamics of the $p$-adic shift and applications. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 209-218. doi: 10.3934/dcds.2011.30.209 [9] Jim Wiseman. Symbolic dynamics from signed matrices. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 621-638. doi: 10.3934/dcds.2004.11.621 [10] George Osipenko, Stephen Campbell. Applied symbolic dynamics: attractors and filtrations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 43-60. doi: 10.3934/dcds.1999.5.43 [11] Michael Hochman. A note on universality in multidimensional symbolic dynamics. Discrete & Continuous Dynamical Systems - S, 2009, 2 (2) : 301-314. doi: 10.3934/dcdss.2009.2.301 [12] Fritz Colonius, Alexandre J. Santana. Topological conjugacy for affine-linear flows and control systems. Communications on Pure & Applied Analysis, 2011, 10 (3) : 847-857. doi: 10.3934/cpaa.2011.10.847 [13] Ming-Chia Li, Ming-Jiea Lyu. Topological conjugacy for Lipschitz perturbations of non-autonomous systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 5011-5024. doi: 10.3934/dcds.2016017 [14] Álvaro Castañeda, Gonzalo Robledo. Dichotomy spectrum and almost topological conjugacy on nonautonomus unbounded difference systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2287-2304. doi: 10.3934/dcds.2018094 [15] Wei Lin, Jianhong Wu, Guanrong Chen. Generalized snap-back repeller and semi-conjugacy to shift operators of piecewise continuous transformations. Discrete & Continuous Dynamical Systems - A, 2007, 19 (1) : 103-119. doi: 10.3934/dcds.2007.19.103 [16] Kingshook Biswas. Complete conjugacy invariants of nonlinearizable holomorphic dynamics. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 847-856. doi: 10.3934/dcds.2010.26.847 [17] Amin Boumenir, Vu Kim Tuan. Reconstruction of the coefficients of a star graph from observations of its vertices. Inverse Problems & Imaging, 2018, 12 (6) : 1293-1308. doi: 10.3934/ipi.2018054 [18] Chris Good, Sergio Macías. What is topological about topological dynamics?. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1007-1031. doi: 10.3934/dcds.2018043 [19] Mario Roy. A new variation of Bowen's formula for graph directed Markov systems. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2533-2551. doi: 10.3934/dcds.2012.32.2533 [20] Jose S. Cánovas, Tönu Puu, Manuel Ruiz Marín. Detecting chaos in a duopoly model via symbolic dynamics. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 269-278. doi: 10.3934/dcdsb.2010.13.269

2018 Impact Factor: 1.143

## Metrics

• HTML views (120)
• Cited by (0)

• on AIMS