American Institute of Mathematical Sciences

Advanced
December  2009, 25(4): 1297-1317. doi: 10.3934/dcds.2009.25.1297

Fixed point shifts of inert involutions

Nicholas Long 1,

1. 

Stephen F. Austin State University, Department of Mathematics and Statistics, P.O. Box 13040, SFA Station, Nacogdoches, TX 75962-3040, United States

Received  February 2009 Revised  June 2009 Published  September 2009

Given a mixing shift of finite type $X$, we consider which subshifts of finite type $Y \subset X$ can be realized as the fixed point shift of an inert involution of $X$. We establish a condition on the periodic points of $X$ and $Y$ that is necessary for $Y$ to be the fixed point shift of an inert involution of $X$. We show that this condition is sufficient to realize $Y$ as the fixed point shift of an involution, up to shift equivalence on $X$, if $X$ is a shift of finite type with Artin-Mazur zeta function equivalent to 1 mod 2. Given an inert involution $f$ of a mixing shift of finite type $X$, we characterize what $f$-invariant subshifts can be realized as the fixed point shift of an inert involution.
Keywords: fixed point shift, inert, Henon, involution, automorphism group..
Mathematics Subject Classification: Primary: 37B10; Secondary: 37C85, 37F10. .
Citation: Nicholas Long. Fixed point shifts of inert involutions. Discrete & Continuous Dynamical Systems, 2009, 25 (4) : 1297-1317. doi: 10.3934/dcds.2009.25.1297
[1]

Van Cyr, John Franks, Bryna Kra, Samuel Petite. Distortion and the automorphism group of a shift. Journal of Modern Dynamics, 2018, 13: 147-161. doi: 10.3934/jmd.2018015
[2]

Van Cyr, Bryna Kra. The automorphism group of a minimal shift of stretched exponential growth. Journal of Modern Dynamics, 2016, 10: 483-495. doi: 10.3934/jmd.2016.10.483
[3]

Hans Koch. A renormalization group fixed point associated with the breakup of golden invariant tori. Discrete & Continuous Dynamical Systems, 2004, 11 (4) : 881-909. doi: 10.3934/dcds.2004.11.881
[4]

Miklós Horváth. Spectral shift functions in the fixed energy inverse scattering. Inverse Problems & Imaging, 2011, 5 (4) : 843-858. doi: 10.3934/ipi.2011.5.843
[5]

Mike Boyle, Sompong Chuysurichay. The mapping class group of a shift of finite type. Journal of Modern Dynamics, 2018, 13: 115-145. doi: 10.3934/jmd.2018014
[6]

Jan J. Sławianowski, Vasyl Kovalchuk, Agnieszka Martens, Barbara Gołubowska, Ewa E. Rożko. Essential nonlinearity implied by symmetry group. Problems of affine invariance in mechanics and physics. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 699-733. doi: 10.3934/dcdsb.2012.17.699
[7]

Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017
[8]

Jorge Groisman. Expansive and fixed point free homeomorphisms of the plane. Discrete & Continuous Dynamical Systems, 2012, 32 (5) : 1709-1721. doi: 10.3934/dcds.2012.32.1709
[9]

Yong Ji, Ercai Chen, Yunping Wang, Cao Zhao. Bowen entropy for fixed-point free flows. Discrete & Continuous Dynamical Systems, 2019, 39 (11) : 6231-6239. doi: 10.3934/dcds.2019271
[10]

Shui-Hung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692-697. doi: 10.3934/proc.2011.2011.692
[11]

Luis Hernández-Corbato, Francisco R. Ruiz del Portal. Fixed point indices of planar continuous maps. Discrete & Continuous Dynamical Systems, 2015, 35 (7) : 2979-2995. doi: 10.3934/dcds.2015.35.2979
[12]

Antonio Garcia. Transition tori near an elliptic-fixed point. Discrete & Continuous Dynamical Systems, 2000, 6 (2) : 381-392. doi: 10.3934/dcds.2000.6.381
[13]

John Erik Fornæss, Brendan Weickert. A quantized henon map. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 723-740. doi: 10.3934/dcds.2000.6.723
[14]

François Gay-Balmaz, Cesare Tronci, Cornelia Vizman. Geometric dynamics on the automorphism group of principal bundles: Geodesic flows, dual pairs and chromomorphism groups. Journal of Geometric Mechanics, 2013, 5 (1) : 39-84. doi: 10.3934/jgm.2013.5.39
[15]

Hongyan Guo. Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra. Electronic Research Archive, 2021, 29 (4) : 2673-2685. doi: 10.3934/era.2021008
[16]

Yilun Shang. Group pinning consensus under fixed and randomly switching topologies with acyclic partition. Networks & Heterogeneous Media, 2014, 9 (3) : 553-573. doi: 10.3934/nhm.2014.9.553
[17]

Cleon S. Barroso. The approximate fixed point property in Hausdorff topological vector spaces and applications. Discrete & Continuous Dynamical Systems, 2009, 25 (2) : 467-479. doi: 10.3934/dcds.2009.25.467
[18]

Teck-Cheong Lim. On the largest common fixed point of a commuting family of isotone maps. Conference Publications, 2005, 2005 (Special) : 621-623. doi: 10.3934/proc.2005.2005.621
[19]

Mircea Sofonea, Cezar Avramescu, Andaluzia Matei. A fixed point result with applications in the study of viscoplastic frictionless contact problems. Communications on Pure & Applied Analysis, 2008, 7 (3) : 645-658. doi: 10.3934/cpaa.2008.7.645
[20]

Parin Chaipunya, Poom Kumam. Fixed point theorems for cyclic operators with application in Fractional integral inclusions with delays. Conference Publications, 2015, 2015 (special) : 248-257. doi: 10.3934/proc.2015.0248

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (85)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences