• Previous Article
    Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations
  • DCDS Home
  • This Issue
  • Next Article
    On the shift differentiability of the flow generated by a hyperbolic system of conservation laws
April  2000, 6(2): 351-360. doi: 10.3934/dcds.2000.6.351

Examples of topologically transitive skew-products

1. 

Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania

Received  March 1999 Revised  September 1999 Published  January 2000

Let $\sigma:\Sigma\to\Sigma$ be a topologically mixing shift of finite type. If $G$ is a group, and $\beta:\Sigma\to G$ is a continuous function, denote by $\sigma_\beta$ the skew-product of $\sigma$ by $\beta$. If $G$ is $\mathbb R^n$, we show examples of continuous multiparameters families of functions $\beta$ for which the skew-products $\sigma_\beta$ are topologically transitive for sets of parameters of full measure. If $G$ is a connected semisimple matrix Lie group, we show examples of functions $\beta$ for which the skew-products $\sigma_beta$ are topologically transitive.
Citation: Viorel Nitica. Examples of topologically transitive skew-products. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 351-360. doi: 10.3934/dcds.2000.6.351
[1]

Eugen Mihailescu, Mariusz Urbański. Transversal families of hyperbolic skew-products. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 907-928. doi: 10.3934/dcds.2008.21.907

[2]

Jose S. Cánovas, Antonio Falcó. The set of periods for a class of skew-products. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 893-900. doi: 10.3934/dcds.2000.6.893

[3]

Núria Fagella, Àngel Jorba, Marc Jorba-Cuscó, Joan Carles Tatjer. Classification of linear skew-products of the complex plane and an affine route to fractalization. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 3767-3787. doi: 10.3934/dcds.2019153

[4]

Morched Boughariou. Closed orbits of Hamiltonian systems on non-compact prescribed energy surfaces. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 603-616. doi: 10.3934/dcds.2003.9.603

[5]

Alain Bensoussan, Jens Frehse, Jens Vogelgesang. Systems of Bellman equations to stochastic differential games with non-compact coupling. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1375-1389. doi: 10.3934/dcds.2010.27.1375

[6]

Mohamed Boulanouar. On a Mathematical model with non-compact boundary conditions describing bacterial population (Ⅱ). Evolution Equations & Control Theory, 2019, 8 (2) : 247-271. doi: 10.3934/eect.2019014

[7]

Rui Gao, Weixiao Shen. Analytic skew-products of quadratic polynomials over Misiurewicz-Thurston maps. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2013-2036. doi: 10.3934/dcds.2014.34.2013

[8]

David Färm, Tomas Persson. Dimension and measure of baker-like skew-products of $\boldsymbol{\beta}$-transformations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (10) : 3525-3537. doi: 10.3934/dcds.2012.32.3525

[9]

Viorel Niţică. Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 1197-1204. doi: 10.3934/dcds.2011.29.1197

[10]

Nikos I. Karachalios, Athanasios N Lyberopoulos. On the dynamics of a degenerate damped semilinear wave equation in \mathbb{R}^N : the non-compact case. Conference Publications, 2007, 2007 (Special) : 531-540. doi: 10.3934/proc.2007.2007.531

[11]

John Banks, Brett Stanley. A note on equivalent definitions of topological transitivity. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1293-1296. doi: 10.3934/dcds.2013.33.1293

[12]

Roy Adler, Bruce Kitchens, Michael Shub. Stably ergodic skew products. Discrete & Continuous Dynamical Systems - A, 1996, 2 (3) : 349-350. doi: 10.3934/dcds.1996.2.349

[13]

Roy Adler, Bruce Kitchens, Michael Shub. Errata to "Stably ergodic skew products". Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 456-456. doi: 10.3934/dcds.1999.5.456

[14]

Àlex Haro. On strange attractors in a class of pinched skew products. Discrete & Continuous Dynamical Systems - A, 2012, 32 (2) : 605-617. doi: 10.3934/dcds.2012.32.605

[15]

Matúš Dirbák. Minimal skew products with hypertransitive or mixing properties. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1657-1674. doi: 10.3934/dcds.2012.32.1657

[16]

Jon Aaronson, Michael Bromberg, Nishant Chandgotia. Rational ergodicity of step function skew products. Journal of Modern Dynamics, 2018, 13: 1-42. doi: 10.3934/jmd.2018012

[17]

C.P. Walkden. Stable ergodicity of skew products of one-dimensional hyperbolic flows. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 897-904. doi: 10.3934/dcds.1999.5.897

[18]

Kohei Ueno. Weighted Green functions of nondegenerate polynomial skew products on $\mathbb{C}^2$. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 985-996. doi: 10.3934/dcds.2011.31.985

[19]

Kohei Ueno. Weighted Green functions of polynomial skew products on $\mathbb{C}^2$. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2283-2305. doi: 10.3934/dcds.2014.34.2283

[20]

Wacław Marzantowicz, Feliks Przytycki. Estimates of the topological entropy from below for continuous self-maps on some compact manifolds. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 501-512. doi: 10.3934/dcds.2008.21.501

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]