American Institute of Mathematical Sciences

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

Minimal subsets of projective flows

Kristian Bjerklöv 1, and  Russell Johnson 2,

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.
Keywords: almost periodic coefficients., projective flows, minimal subsets, Li-Yorke chaos.
Mathematics Subject Classification: Primary: 37B55, 37D25, 34C2.
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]

Daniel Gonçalves, Bruno Brogni Uggioni. Li-Yorke Chaos for ultragraph shift spaces. Discrete & Continuous Dynamical Systems - A, 2020, 40 (4) : 2347-2365. doi: 10.3934/dcds.2020117
[2]

Ghassen Askri. Li-Yorke chaos for dendrite maps with zero topological entropy and ω-limit sets. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 2957-2976. doi: 10.3934/dcds.2017127
[3]

Jakub Šotola. Relationship between Li-Yorke chaos and positive topological sequence entropy in nonautonomous dynamical systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 5119-5128. doi: 10.3934/dcds.2018225
[4]

Yuanfen Xiao. Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for $ \beta $-transformation. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020267
[5]

Tomás Caraballo, David Cheban. Almost periodic and asymptotically almost periodic solutions of Liénard equations. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 703-717. doi: 10.3934/dcdsb.2011.16.703
[6]

Hiromichi Nakayama, Takeo Noda. Minimal sets and chain recurrent sets of projective flows induced from minimal flows on $3$-manifolds. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 629-638. doi: 10.3934/dcds.2005.12.629
[7]

Xiao Wang, Zhaohui Yang, Xiongwei Liu. Periodic and almost periodic oscillations in a delay differential equation system with time-varying coefficients. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6123-6138. doi: 10.3934/dcds.2017263
[8]

Jaroslav Smítal, Marta Štefánková. Omega-chaos almost everywhere. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1323-1327. doi: 10.3934/dcds.2003.9.1323
[9]

Motahhareh Gharahi, Shahram Khazaei. Reduced access structures with four minimal qualified subsets on six participants. Advances in Mathematics of Communications, 2018, 12 (1) : 199-214. doi: 10.3934/amc.2018014
[10]

James Nolen, Jack Xin. Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle. Discrete & Continuous Dynamical Systems - A, 2005, 13 (5) : 1217-1234. doi: 10.3934/dcds.2005.13.1217
[11]

Dou Dou, Meng Fan, Hua Qiu. Topological entropy on subsets for fixed-point free flows. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6319-6331. doi: 10.3934/dcds.2017273
[12]

Francesco Maggi, Salvatore Stuvard, Antonello Scardicchio. Soap films with gravity and almost-minimal surfaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (12) : 6877-6912. doi: 10.3934/dcds.2019236
[13]

José Ginés Espín Buendía, Daniel Peralta-salas, Gabriel Soler López. Existence of minimal flows on nonorientable surfaces. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4191-4211. doi: 10.3934/dcds.2017178
[14]

Lidong Wang, Hui Wang, Guifeng Huang. Minimal sets and $\omega$-chaos in expansive systems with weak specification property. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 1231-1238. doi: 10.3934/dcds.2015.35.1231
[15]

Víctor Jiménez López, Gabriel Soler López. A topological characterization of ω-limit sets for continuous flows on the projective plane. Conference Publications, 2001, 2001 (Special) : 254-258. doi: 10.3934/proc.2001.2001.254
[16]

Wenbin Liu, Zhaosheng Feng. Periodic solutions for $p$-Laplacian systems of Liénard-type. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1393-1400. doi: 10.3934/cpaa.2011.10.1393
[17]

Tiantian Ma, Zaihong Wang. Periodic solutions of Liénard equations with resonant isochronous potentials. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1563-1581. doi: 10.3934/dcds.2013.33.1563
[18]

Peter Giesl, Martin Rasmussen. A note on almost periodic variational equations. Communications on Pure & Applied Analysis, 2011, 10 (3) : 983-994. doi: 10.3934/cpaa.2011.10.983
[19]

Gernot Greschonig. Real cocycles of point-distal minimal flows. Conference Publications, 2015, 2015 (special) : 540-548. doi: 10.3934/proc.2015.0540
[20]

Ronald A. Knight. Compact minimal sets in continuous recurrent flows. Conference Publications, 1998, 1998 (Special) : 397-407. doi: 10.3934/proc.1998.1998.397

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (21)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences