A variational principle for impulsive semiflows

Alves, José F.; Carvalho, Maria; Vásquez, Carlos H.

doi:10.1016/j.jde.2015.05.017

Cited by 15 publications

(20 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By Lemma 5.2, we have that τ * is continuous on X ξ . Applying Proposition 4.3 in [3] we obtain the continuity of the semiflowφ.…”

Section: Let Us Considermentioning

confidence: 89%

“…Motivated by this problem, one can try to find variations of Bowen's definitions of topological entropies that can be applied to the study of not necessarily continuous semiflows. In this direction, Alves, Carvalho and Vásquez ( [3]) have introduced the notion of topological τ -entropy, which depends on an admissible function τ . Their definition only makes use of separated sets.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Topological entropy for discontinuous semiflows

Nelda

Martín

2019

Journal of Differential Equations

View full text Add to dashboard Cite

We study two variations of Bowen's definitions of topological entropy based on separated and spanning sets which can be applied to the study of discontinuous semiflows on compact metric spaces. We prove that these definitions reduce to Bowen's ones in the case of continuous semiflows. As a second result, we prove that our entropies give a lower bound for the τ -entropy defined by Alves, Carvalho and Vásquez (2015). Finally, we prove that for impulsive semiflows satisfying certain regularity condition, there exists a continuous semiflow defined on another compact metric space which is related to the first one by a semiconjugation, and whose topological entropy equals our extended notion of topological entropy by using separated sets for the original semiflow.

show abstract

“…By Lemma 5.2, we have that τ * is continuous on X ξ . Applying Proposition 4.3 in [3] we obtain the continuity of the semiflowφ.…”

Section: Let Us Considermentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Topological entropy for discontinuous semiflows

Nelda

Martín

2019

Journal of Differential Equations

View full text Add to dashboard Cite

show abstract

“…The study of chaotic dynamical systems presents several difficult problems as, for example, to estimate the topological entropy as can be seen in [4,5,11,21] and, with more recent approaches, in [1,2,6]. Some systems are known to have positive topological entropy.…”

Section: Introductionmentioning

confidence: 99%

Polynomial entropy and expansivity

2017

View full text Add to dashboard Cite

In this paper we study the polynomial entropy of homeomorphism on compact metric space. We construct a homeomorphism on a compact metric space with vanishing polynomial entropy that it is not equicontinuous. Also we give examples with arbitrarily small polynomial entropy. Finally, we show that expansive homeomorphisms and positively expansive maps of compact metric spaces with infinitely many points have polynomial entropy greater or equal than 1.

show abstract

“…So far, a useful approach has been to use potentials and finding equilibrium states. However, as the classical notion of topological entropy requires continuity and impulsive semiflows exhibit discontinuities, it became necessary to introduce a generalized concept of topological entropy, and this has been done in [2]. Moreover, it was proved that the new notion coincides with the classical one for continuous semiflows, and also a partial variational principle for impulsive semiflows: the topological entropy coincides with the supremum of the metric entropies of time-one maps.…”

Section: Introductionmentioning

confidence: 99%