Geodesic
Exponentially splittable hyperbolic systems with two independent variables
Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 335-349

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A property of hyperbolic systems which is an analogue of the property of exponential dichotomy for ordinary differential equations is studied. Exponentially decaying Green matrices of first and second kind are the main tool. Bounded solutions of e-splittable systems and projections in phase space of the Cauchy problem which describe the dichotomy of the solutions are constructed; the equivalence of the properties of e-splittability and regularity and preservation of e-splittability under small perturbations of the system are established. Bibliography: 11 titles. 
@article{SM_1988_61_2_a4,
     author = {R. K. Romanovskii},
     title = {Exponentially splittable hyperbolic systems with two independent variables},
     journal = {Sbornik. Mathematics},
     pages = {335--349},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_2_a4/}
}
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R. K. Romanovskii. Exponentially splittable hyperbolic systems with two independent variables. Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 335-349. http://geodesic.mathdoc.fr/item/SM_1988_61_2_a4/