Commutativity and non-commutativity of topological sequence entropy

Balibrea, Francisco; Peña, José Salvador Cánovas; López, Vı́ctor Jiménez

doi:10.5802/aif.1735

Cited by 15 publications

(4 citation statements)

References 10 publications

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“…Inspired by [Kolyada & Snoha, 1996], the commutativity or non-commutativity of other types of entropy such sequence entropy were proved in [Balibrea et al, 1999a, Balibrea et al, 1999b). …”

Section: Topological Entropymentioning

confidence: 99%

Recent Developments in Dynamical Systems: Three Perspectives

Balibrea

Caraballo

Kloeden

et al. 2010

Int. J. Bifurcation Chaos

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The aim of this paper is to give an account of some problems considered in past years in the setting of Dynamical Systems, some new research directions and also state some open problems Keywords: Topological entropy, Li-Yorke chaos, Lyapunov exponent, continua, nonautonomous systems, difference equations, ordinary and partial differential equations, set-valued dynamical system, global attractor, non-autonomous and random pullback attractors.

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“…Inspired by [Kolyada & Snoha, 1996], the commutativity or non-commutativity of other types of entropy such sequence entropy were proved in [Balibrea et al, 1999a, Balibrea et al, 1999b). …”

Section: Topological Entropymentioning

confidence: 99%

Recent Developments in Dynamical Systems: Three Perspectives

Balibrea

Caraballo

Kloeden

et al. 2010

Int. J. Bifurcation Chaos

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“…However, there are several properties that are held only for one of the compositions. For instance, their topological sequence entropies do not agree in general (see [3]) or one composition is transitive (there exists a dense orbit) while the other composition is not transitive, as the following example shows. Let X = [0, 1] and consider the maps 2 3 ].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 88%

On the dynamics of composition of commuting interval maps

Cánovas

Linero

2005

Journal of Mathematical Analysis and Applications

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“…Assume the contrary: let n G N be such that f\ Kg is monotonic for any 0 € {0,1}". Then (f\K g ) 2 " has at most periodic points of period 2 and this leads to a contradiction because [J Kg could not contain { an infinite w-limit set of / . So the number of maximal solenoids is smaller than k and the proof is complete.…”

Section: A I N Resultsmentioning

confidence: 99%