Bounds for invariance pressure

Colonius, Fritz; Cossich, João A. N.; Santana, Alexandre J.

doi:10.1016/j.jde.2019.11.091

Cited by 13 publications

(7 citation statements)

References 18 publications

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“…Invariance pressure, as a generalization of invariance entropy, was first introduced by Colonius, Santana, and Cossich [8,4]. Recently, the same authors in [7] obtain some bounds of invariance pressure and get an explicit formula for hyperbolic linear control systems. Zhong and Huang [19] introduced a version of invariance pressure in a way resembling Hausdorff dimension, which is called Bowen invariance pressure.…”

Section: (Communicated By Xiangdong Ye)mentioning

confidence: 99%

Variational principles of invariance pressures on partitions

Zhong¹

2020

Discrete &Amp; Continuous Dynamical Systems - A

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1. Introduction. Topological feedback entropy was first introduced by Nair et al. [14] by using invariant open covers to characterize the minimal data rate for making a subset of the state space invariant. Later, Colonius and Kawan [5] introduced invariance entropy, which is defined via spanning sets, to describe the exponential growth rate of the minimal number of different control functions sufficient for orbits to stay in a given set when starting in a subset of this set. The fact that these two entropies are equivalent was shown by Colonius, Kawan, and Nair [6]. Recently, Huang and Zhong [10] use the theory of Carathéodory-Pesin structure to obtain a dimension-like characterization for invariance entropy, which is called Bowen invariance entropy. We refer the reader to the monograph written by Kawan [11] for more about invariance entropy.By choosing conditionally invariant measures and quasi-stationary measures, Colonius [2, 3] first introduced four notions of metric invariance entropy in analogy to the topological notion of invariance entropy of deterministic control systems. In [2], Colonius showed that the metric entropy of a given controlled invariant set coincides with the minimal entropy of coder-controllers associated with a quasi-stationary measure rendering that set invariant. Variational principle [17] for topological entropy [1] and measure theoretic entropy [12] in classical dynamical systems states that topological entropy is determined by the supremum of measure theoretic entropies. Feng and Huang gave variational principles between Bowen 2010 Mathematics Subject Classification. Primary: 37A35, 37B40, 37C45; Secondary: 93C55.

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Section: (Communicated By Xiangdong Ye)mentioning

confidence: 99%

Variational principles of invariance pressures on partitions

Zhong¹

2020

Discrete &Amp; Continuous Dynamical Systems - A

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“…Theorem 15 Consider the control system given by (3) and suppose that the system without control restriction is controllable.…”

Section: Lemma 14 Ifmentioning

confidence: 99%

“…Theorems 18 and 20. The proof uses arguments from [3] which in turn are based on a construction by Kawan [8,Theorem 4.3], [9, Theorem 5.1] (for the discrete-time case cf. also [9,Remark 5.4] and Nair, Evans, Mareels, Moran [12,Theorem 3]).…”

Section: Invariance Pressure For Linear Systemsmentioning

confidence: 99%

Invariance pressure for linear discrete-time systems

Colonius

Cossich

Santana

2019

2019 IEEE Information Theory Workshop (ITW)

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“…Measuretheoretic versions of invariance entropy have been considered in Colonius [4] and Wang et al [15]. Invariance pressure has been analyzed in Colonius et al [1][2][3]. In Zhong and Huang [18] it is shown that several generalized notions of invariance pressure fit into the dimensiontheoretic framework due to Pesin.…”

Section: Introductionmentioning

confidence: 99%