American Institute of Mathematical Sciences

Advanced
July  2006, 14(3): 447-463. doi: 10.3934/dcds.2006.14.447

Fundamental semigroups for dynamical systems

Fritz Colonius 1, and  Marco Spadini 2,

1. 

Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
2. 

Dipartimento di Matematica Applicata, Via S. Marta 3, 50139 Firenze, Italy

Received  August 2004 Revised  July 2005 Published  December 2005

Algebraic semigroups describing the dynamic behavior are associated to compact, locally maximal chain transitive subsets. The construction is based on perturbations and associated local control sets. The dependence on the perturbation structure is analyzed.
Keywords: perturbation structure, algebraic semigroups., Chain transitive subsets, local control sets.
Mathematics Subject Classification: 37N35, 93C10, 93C15, 20M9.
Citation: Fritz Colonius, Marco Spadini. Fundamental semigroups for dynamical systems. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 447-463. doi: 10.3934/dcds.2006.14.447
[1]

Victor Ayala, Adriano Da Silva, Luiz A. B. San Martin. Control systems on flag manifolds and their chain control sets. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2301-2313. doi: 10.3934/dcds.2017101
[2]

Shengzhi Zhu, Shaobo Gan, Lan Wen. Indices of singularities of robustly transitive sets. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 945-957. doi: 10.3934/dcds.2008.21.945
[3]

Mykola Matviichuk, Damoon Robatian. Chain transitive induced interval maps on continua. Discrete and Continuous Dynamical Systems, 2015, 35 (2) : 741-755. doi: 10.3934/dcds.2015.35.741
[4]

Olexiy V. Kapustyan, Pavlo O. Kasyanov, José Valero. Chain recurrence and structure of $ \omega $-limit sets of multivalued semiflows. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2197-2217. doi: 10.3934/cpaa.2020096
[5]

Ming Li, Shaobo Gan, Lan Wen. Robustly transitive singular sets via approach of an extended linear Poincaré flow. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 239-269. doi: 10.3934/dcds.2005.13.239
[6]

Geir Bogfjellmo. Algebraic structure of aromatic B-series. Journal of Computational Dynamics, 2019, 6 (2) : 199-222. doi: 10.3934/jcd.2019010
[7]

Boris Hasselblatt and Jorg Schmeling. Dimension product structure of hyperbolic sets. Electronic Research Announcements, 2004, 10: 88-96.

[8]

Juan Wang, Xiaodan Zhang, Yun Zhao. Dimension estimates for arbitrary subsets of limit sets of a Markov construction and related multifractal analysis. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2315-2332. doi: 10.3934/dcds.2014.34.2315
[9]

José Ginés Espín Buendía, Víctor Jiménez Lopéz. A topological characterization of the $\omega$-limit sets of analytic vector fields on open subsets of the sphere. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1143-1173. doi: 10.3934/dcdsb.2019010
[10]

Heinz Schättler, Urszula Ledzewicz. Perturbation feedback control: A geometric interpretation. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 631-654. doi: 10.3934/naco.2012.2.631
[11]

Rich Stankewitz, Hiroki Sumi. Random backward iteration algorithm for Julia sets of rational semigroups. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2165-2175. doi: 10.3934/dcds.2015.35.2165
[12]

Rich Stankewitz, Hiroki Sumi. Backward iteration algorithms for Julia sets of Möbius semigroups. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6475-6485. doi: 10.3934/dcds.2016079
[13]

Hiroki Sumi, Mariusz Urbański. Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 313-363. doi: 10.3934/dcds.2011.30.313
[14]

Hiroki Sumi. Dynamics of postcritically bounded polynomial semigroups I: Connected components of the Julia sets. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1205-1244. doi: 10.3934/dcds.2011.29.1205
[15]

Alberto A. Pinto, João P. Almeida, Telmo Parreira. Local market structure in a Hotelling town. Journal of Dynamics and Games, 2016, 3 (1) : 75-100. doi: 10.3934/jdg.2016004
[16]

Irene Márquez-Corbella, Edgar Martínez-Moro. Algebraic structure of the minimal support codewords set of some linear codes. Advances in Mathematics of Communications, 2011, 5 (2) : 233-244. doi: 10.3934/amc.2011.5.233
[17]

Peter Müller, Gábor P. Nagy. On the non-existence of sharply transitive sets of permutations in certain finite permutation groups. Advances in Mathematics of Communications, 2011, 5 (2) : 303-308. doi: 10.3934/amc.2011.5.303
[18]

Jonathan Meddaugh, Brian E. Raines. The structure of limit sets for $\mathbb{Z}^d$ actions. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4765-4780. doi: 10.3934/dcds.2014.34.4765
[19]

Magdalena Foryś-Krawiec, Jana Hantáková, Piotr Oprocha. On the structure of α-limit sets of backward trajectories for graph maps. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1435-1463. doi: 10.3934/dcds.2021159
[20]

Tomasz Komorowski, Łukasz Stȩpień. Kinetic limit for a harmonic chain with a conservative Ornstein-Uhlenbeck stochastic perturbation. Kinetic and Related Models, 2018, 11 (2) : 239-278. doi: 10.3934/krm.2018013

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (64)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy