American Institute of Mathematical Sciences

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2003, 2003(Special): 960-966. doi: 10.3934/proc.2003.2003.960

Formally gradient reaction-diffusion systems in Rn have zero spatio-temporal topological

Zelik S. 1,

1. 

Université de Poitiers, Laboratoire d’Applications des Mathématiques - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, 86962 Chasseneuil Futuroscope Cedex, France

Received  August 2002 Published  April 2003

We prove that the spatio-temporal topological entropy (= the topological entropy per unit volume) is equal to zero for formally gradient reaction-diffusion systems in $\mathbb(R)^n$. This result generalizes the well-known fact that gradient ODEs have zero topological entropy.
Keywords: Reaction-diffusion systems, unbounded domains, topological entropy., formally gradient systems.
Mathematics Subject Classification: 35B40, 35B4.
Citation: Zelik S.. Formally gradient reaction-diffusion systems in Rn have zero spatio-temporal topological. Conference Publications, 2003, 2003 (Special) : 960-966. doi: 10.3934/proc.2003.2003.960
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