
Previous Article
Convergence to square waves for a price model with delay
 DCDS Home
 This Issue

Next Article
Moments and lower bounds in the farfield of solutions to quasigeostrophic flows
Polymorphisms, Markov processes, quasisimilarity
1.  St. Petersburg Department of Steklov Institute of Mathematics, 27 Fontanka, St. Petersburg, 191023, Russian Federation 
The question is as follows: is it possible to have a quasisimilarity between a measurepreserving automorphism $T$ and a polymorphism $\Pi$ (that is not an automorphism)? In less definite terms: what kind of equivalence can exist between deterministic and random (Markov) dynamical systems? We give the answer: every nonmixing prime polymorphism is quasisimilar to an automorphism with positive entropy, and every $K$automorphism $T$ is quasisimilar to a polymorphism $\Pi$ that is a special random perturbation of the automorphism $T$.
[1] 
Haritha C, Nikita Agarwal. Product of expansive Markov maps with hole. Discrete & Continuous Dynamical Systems  A, 2019, 39 (10) : 57435774. doi: 10.3934/dcds.2019252 
[2] 
B. Fernandez, E. Ugalde, J. Urías. Spectrum of dimensions for Poincaré recurrences of Markov maps. Discrete & Continuous Dynamical Systems  A, 2002, 8 (4) : 835849. doi: 10.3934/dcds.2002.8.835 
[3] 
Xu Zhang, Yuming Shi, Guanrong Chen. Coupledexpanding maps under small perturbations. Discrete & Continuous Dynamical Systems  A, 2011, 29 (3) : 12911307. doi: 10.3934/dcds.2011.29.1291 
[4] 
Yujun Zhu. Topological quasistability of partially hyperbolic diffeomorphisms under random perturbations. Discrete & Continuous Dynamical Systems  A, 2014, 34 (2) : 869882. doi: 10.3934/dcds.2014.34.869 
[5] 
Xin Zhang, Shuangling Yang. Complex dynamics in a quasiperiodic plasma perturbations model. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020272 
[6] 
Marco Lenci. Uniformly expanding Markov maps of the real line: Exactness and infinite mixing. Discrete & Continuous Dynamical Systems  A, 2017, 37 (7) : 38673903. doi: 10.3934/dcds.2017163 
[7] 
Manuela Giampieri, Stefano Isola. A oneparameter family of analytic Markov maps with an intermittency transition. Discrete & Continuous Dynamical Systems  A, 2005, 12 (1) : 115136. doi: 10.3934/dcds.2005.12.115 
[8] 
Paweł Góra, Abraham Boyarsky. Stochastic perturbations and Ulam's method for Wshaped maps. Discrete & Continuous Dynamical Systems  A, 2013, 33 (5) : 19371944. doi: 10.3934/dcds.2013.33.1937 
[9] 
Marina Gonchenko, Sergey Gonchenko, Klim Safonov. Reversible perturbations of conservative Hénonlike maps. Discrete & Continuous Dynamical Systems  A, 2020 doi: 10.3934/dcds.2020343 
[10] 
Qihuai Liu, Dingbian Qian, Zhiguo Wang. Quasiperiodic solutions of the LotkaVolterra competition systems with quasiperiodic perturbations. Discrete & Continuous Dynamical Systems  B, 2012, 17 (5) : 15371550. doi: 10.3934/dcdsb.2012.17.1537 
[11] 
Junxiang Xu. On quasiperiodic perturbations of hyperbolictype degenerate equilibrium point of a class of planar systems. Discrete & Continuous Dynamical Systems  A, 2013, 33 (6) : 25932619. doi: 10.3934/dcds.2013.33.2593 
[12] 
Jie Liu, Jianguo Si. Invariant tori of a nonlinear Schrödinger equation with quasiperiodically unbounded perturbations. Communications on Pure & Applied Analysis, 2017, 16 (1) : 2568. doi: 10.3934/cpaa.2017002 
[13] 
Jose F. Alves; Stefano Luzzatto and Vilton Pinheiro. Markov structures for nonuniformly expanding maps on compact manifolds in arbitrary dimension. Electronic Research Announcements, 2003, 9: 2631. 
[14] 
Marat Akhmet, Ejaily Milad Alejaily. Abstract similarity, fractals and chaos. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020191 
[15] 
Jinjing Jiao, Guanghua Shi. Quasiperiodic solutions for the twodimensional systems with an elliptictype degenerate equilibrium point under small perturbations. Communications on Pure & Applied Analysis, 2020, 19 (11) : 51575180. doi: 10.3934/cpaa.2020231 
[16] 
Àlex Haro, Rafael de la Llave. A parameterization method for the computation of invariant tori and their whiskers in quasiperiodic maps: Numerical algorithms. Discrete & Continuous Dynamical Systems  B, 2006, 6 (6) : 12611300. doi: 10.3934/dcdsb.2006.6.1261 
[17] 
Àngel Jorba, Pau Rabassa, Joan Carles Tatjer. Superstable periodic orbits of 1d maps under quasiperiodic forcing and reducibility loss. Discrete & Continuous Dynamical Systems  A, 2014, 34 (2) : 589597. doi: 10.3934/dcds.2014.34.589 
[18] 
Àngel Jorba, Joan Carles Tatjer. A mechanism for the fractalization of invariant curves in quasiperiodically forced 1D maps. Discrete & Continuous Dynamical Systems  B, 2008, 10 (2&3, September) : 537567. doi: 10.3934/dcdsb.2008.10.537 
[19] 
Vassilis G. Papanicolaou, Kyriaki Vasilakopoulou. Similarity solutions of a multidimensional replicator dynamics integrodifferential equation. Journal of Dynamics & Games, 2016, 3 (1) : 5174. doi: 10.3934/jdg.2016003 
[20] 
Jose Carlos Camacho, Maria de los Santos Bruzon. Similarity reductions of a nonlinear model for vibrations of beams. Conference Publications, 2015, 2015 (special) : 176184. doi: 10.3934/proc.2015.0176 
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]