Growth Rates for Semiflows on Hausdorff Spaces

Autor(es)

Kawan, Christoph ^[1] ; Stender, Torben ^[1]

Afiliação do(s) autor(es)

^[1] Univ Augsburg, Inst Math, D-86159 Augsburg - Germany

• Tipo de documento: Artigo Científico
• Fonte: Journal of Dynamics and Differential Equations; v. 24, n. 2, p. 369-390, JUN 2012.
• Citações Web of Science: 3

Resumo

In this paper, we present a theory of vector-valued growth rates for discrete- and continuous-time semiflows on Hausdorff spaces. For a given compact flow-invariant set and an associated growth rate, we introduce the uniform growth spectrum over , and associated real-valued spectra via projections of the vector-valued spectrum onto one-dimensional subspaces. We show that these real-valued spectra are closed intervals if is additionally connected. We also define the Morse spectrum associated with a growth rate by evaluating the growth rate along chains. Moreover, we relate the uniform growth spectrum to the Morse spectrum and we analyze the meaning of limit sets for the long similar to me behavior of growth rates. (AU)

• Processo FAPESP: 11/03140-2 - Entropia de invariância para sistemas de controle em variedades flag e espaços homogêneos
• Beneficiário: Christoph Kawan
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado