May  2008, 9(3&4, May): 493-516. doi: 10.3934/dcdsb.2008.9.493

Minimal subsets of projective flows

1. 

Department of Mathematics and Statistics, Queen's University, Kingston, ON Canada K7L 3N6, Canada

2. 

Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S. Marta 3, 50139 Firenze

Received  January 2007 Revised  June 2007 Published  February 2008

We study the minimal subsets of the projective flow defined by a two-dimensional linear differential system with almost periodic coefficients. We show that such a minimal set may exhibit Li-Yorke chaos and discuss specific examples in which this phenomenon is present. We then give a classification of these minimal sets, and use it to discuss the bounded mean motion property relative to the projective flow.
Citation: Kristian Bjerklöv, Russell Johnson. Minimal subsets of projective flows. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 493-516. doi: 10.3934/dcdsb.2008.9.493
[1]

Mengyu Cheng, Zhenxin Liu. Periodic, almost periodic and almost automorphic solutions for SPDEs with monotone coefficients. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021026

[2]

Yuanfen Xiao. Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for $ \beta $-transformation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 525-536. doi: 10.3934/dcds.2020267

[3]

Amira M. Boughoufala, Ahmed Y. Abdallah. Attractors for FitzHugh-Nagumo lattice systems with almost periodic nonlinear parts. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1549-1563. doi: 10.3934/dcdsb.2020172

[4]

Yi Guan, Michal Fečkan, Jinrong Wang. Periodic solutions and Hyers-Ulam stability of atmospheric Ekman flows. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1157-1176. doi: 10.3934/dcds.2020313

[5]

Yongjie Wang, Nan Gao. Some properties for almost cellular algebras. Electronic Research Archive, 2021, 29 (1) : 1681-1689. doi: 10.3934/era.2020086

[6]

Meng Chen, Yong Hu, Matteo Penegini. On projective threefolds of general type with small positive geometric genus. Electronic Research Archive, , () : -. doi: 10.3934/era.2020117

[7]

Paul A. Glendinning, David J. W. Simpson. A constructive approach to robust chaos using invariant manifolds and expanding cones. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020409

[8]

Xianwei Chen, Xiangling Fu, Zhujun Jing. Chaos control in a special pendulum system for ultra-subharmonic resonance. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 847-860. doi: 10.3934/dcdsb.2020144

[9]

Vivina Barutello, Gian Marco Canneori, Susanna Terracini. Minimal collision arcs asymptotic to central configurations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 61-86. doi: 10.3934/dcds.2020218

[10]

Patrick Martinez, Judith Vancostenoble. Lipschitz stability for the growth rate coefficients in a nonlinear Fisher-KPP equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 695-721. doi: 10.3934/dcdss.2020362

[11]

Jong Yoon Hyun, Boran Kim, Minwon Na. Construction of minimal linear codes from multi-variable functions. Advances in Mathematics of Communications, 2021, 15 (2) : 227-240. doi: 10.3934/amc.2020055

[12]

Chaman Kumar. On Milstein-type scheme for SDE driven by Lévy noise with super-linear coefficients. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1405-1446. doi: 10.3934/dcdsb.2020167

[13]

Zheng Han, Daoyuan Fang. Almost global existence for the Klein-Gordon equation with the Kirchhoff-type nonlinearity. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020287

[14]

Dan Zhu, Rosemary A. Renaut, Hongwei Li, Tianyou Liu. Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory. Inverse Problems & Imaging, 2021, 15 (1) : 159-183. doi: 10.3934/ipi.2020076

[15]

Bo Chen, Youde Wang. Global weak solutions for Landau-Lifshitz flows and heat flows associated to micromagnetic energy functional. Communications on Pure & Applied Analysis, 2021, 20 (1) : 319-338. doi: 10.3934/cpaa.2020268

[16]

Luca Battaglia, Francesca Gladiali, Massimo Grossi. Asymptotic behavior of minimal solutions of $ -\Delta u = \lambda f(u) $ as $ \lambda\to-\infty $. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 681-700. doi: 10.3934/dcds.2020293

[17]

Helmut Abels, Andreas Marquardt. On a linearized Mullins-Sekerka/Stokes system for two-phase flows. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020467

[18]

Martin Heida, Stefan Neukamm, Mario Varga. Stochastic homogenization of $ \Lambda $-convex gradient flows. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 427-453. doi: 10.3934/dcdss.2020328

[19]

Giulia Luise, Giuseppe Savaré. Contraction and regularizing properties of heat flows in metric measure spaces. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 273-297. doi: 10.3934/dcdss.2020327

[20]

Luis Caffarelli, Fanghua Lin. Nonlocal heat flows preserving the L2 energy. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 49-64. doi: 10.3934/dcds.2009.23.49

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (26)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]