In this paper we consider three concepts of uniform exponential trichotomy on the half-line in the general framework of evolution operators in Banach spaces. We obtain a systematic classification of uniform exponential trichotomy concepts and the connections between them.
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 M.-G. Babuţia T. Ceauşu and N. M. Seimeanu On uniform exponential dichotomy of evolution operators Analele Universităţii de Vest Timişoara Seria Matematică - Informatică L (2012) 3-14
 L. Barreira and C. Valls Robustness of nonuniform exponential trichotomies in Banach spaces J. Math. Anal. Appl. 351 (2009) 373-381
 L. Barreira and C. Valls Lyapunov functions for trichotomies with growth rates J. Differential Equations 246 (2009) 1235-1263
 S. Elaidy and O. Hajek Exponential trichotomy of differential systems J. Math.Anal. Appl. 129 (1988) 362-374
 J. Hong Exponential trichotomy and uniformly characteristic exponents of differ- ential systems Ann. Diferential Equations 7 (1991) 272-277
 I. Lopez-Fenner and M. Pinto (hk)- trichotomy and asymptotics of nonau- tonomous differential equations Comp. Math. Appl. 33 (1997) 105-124
 X. Liu Exponential trichotomy and homoclinic bifurcation with saddle-center equi- librium Appl. Math. Lett. 23 (2010)
 N. Lupa and M. Megan Generalized exponential trichotomies for abstract evolu- tion operators on the real line Journal of Function Spaces and Applications 2013 Article ID 409049
 M. Megan and C. Stoica On uniform exponential trichotomy of evolution opera- tors in Banach spaces Integral Equations Operator Theory 60 (2008) 499-506
 M. Megan and C. Stoica Equivalent definitions for uniform exponential tri- chotomy of evolution operators in Banach spaces Hot Topics in Operator Theory Theta Series in Advanced Mathematics 9 (2008) 151-158
 B. Sasu and A. L. Sasu Exponential trichotomy and p-admissibility for evolution families on the real line Math. Z. 253 (2006) 515-536