POSITIVE LINEAR SYSTEMS

By ANDREW DAVIS

CONTENTS GEOMETRIC BACKGROUND SOME CLASSES OF UNIVALENT FUNCTIONS STARLIKE FUNCTIONS CLASS S?[0] NEVANLINNA’S CONDITION CLASSES S?[?], ? ?? HUMMEL’S REPRESENTATION SPIRALLIKE FUNCTIONS ?SPA?CEK’S CONDITION CLOSE-TO-CONVEX AND ?-LIKE FUNCTIONS BOUNDARY BEHAVIOR OF HOLOMORPHIC FUNCTIONS THE JULIA–WOL?–CARATH´EODORY AND DENJOY–WOL?THEOREMS FUNCTIONS OF POSITIVE REAL PART DYNAMIC APPROACH SEMIGROUPS AND GENERATORS FLOW INVARIANCE CONDITIONS AND PARAMETRIC REPRESENTATIONS OF SEMIGROUP GENERATORS THE DENJOY–WOL?AND JULIA–WOL?–CARATH´EODORY THEOREMS FOR SEMIGROUPS GENERATORS WITH BOUNDARY NULL POINTS UNIVALENT FUNCTIONS AND SEMI-COMPLETE VECTOR ?ELDS STARLIKE FUNCTIONS WITH RESPECT TO A BOUNDARY POINT ROBERTSON’S CLASSES ROBERTSON’S CONJECTURE AUXILIARY LEMMAS A GENERALIZATION OF ROBERTSON’S CONJECTURE ANGLE DISTORTION THEOREMS SMALLEST EXTERIOR WEDGE BIGGEST INTERIOR WEDGE FUNCTIONS CONVEX IN ONE DIRECTION SPIRALLIKE FUNCTIONS WITH RESPECT TO A BOUNDARY POINT SPIRALLIKE DOMAINS WITH RESPECT TO A BOUNDARY POINT A CHARACTERIZATION OF SPIRALLIKE FUNCTIONS WITH RESPECT TO A BOUNDARY POINT SUBORDINATION CRITERIA FOR THE CLASS SPIRAL?[1] DISTORTION THEOREMS ‘SPIRAL ANGLE’ DISTORTION THEOREMS GROWTH ESTIMATES FOR SEMIGROUP GENERATORS GROWTH ESTIMATES FOR SPIRALLIKE FUNCTIONS CLASSES G(?, ?) COVERING THEOREMS FOR STARLIKE AND SPIRALLIKE FUNCTIONS KŒNIGS TYPE STARLIKE AND SPIRALLIKE FUNCTIONS SCHR¨ODER’S AND ABEL’S EQUATIONS REMARKS ON STOCHASTIC BRANCHING PROCESSES KŒNIGS’ LINEARIZATION MODEL FOR DILATION TYPE SEMIGROUPS EMBEDDINGS VALIRON’S TYPE LINEARIZATION MODELS FOR HYPERBOLIC TYPE SEMIGROUPS EMBEDDINGS POMMERENKE’S AND BAKER–POMMERENKE’S LINEARIZATION MODELS FOR SEMIGROUPS WITH A BOUNDARY SINK POINT POMMERENKE’S LINEARIZATION MODEL FOR AUTOMORPHIC TYPE MAPPINGS BAKER–POMMERENKE’S MODEL FOR NON-AUTOMORPHIC TYPE SELF-MAPPINGS HIGHER ORDER ANGULAR DI?ERENTIABILITY AT BOUNDARY ?XED POINTS A UNI?ED MODEL EMBEDDING PROPERTY VIA ABEL’S EQUATION RIGIDITY OF HOLOMORPHIC MAPPINGS AND COMMUTING SEMIGROUPS THE BURNS–KRANTZ THEOREM RIGIDITY OF SEMIGROUP GENERATORS COMMUTING SEMIGROUPS OF HOLOMORPHIC MAPPINGS IDENTITY PRINCIPLES FOR COMMUTING SEMIGROUPS DILATION TYPE HYPERBOLIC TYPE PARABOLIC TYPE ASYMPTOTIC BEHAVIOR OF ONE-PARAMETER SEMIGROUPS DILATION CASE GENERAL REMARKS AND RATES OF CONVERGENCE ARGUMENT RIGIDITY PRINCIPLE HYPERBOLIC CASE CRITERIA FOR THE EXPONENTIAL CONVERGENCE ANGULAR SIMILARITY PRINCIPLE PARABOLIC CASE DISCRETE CASE CONTINUOUS CASE UNIVERSAL ASYMPTOTES BACKWARD FLOW INVARIANT DOMAINS FOR SEMIGROUPS EXISTENCE MAXIMAL FIDS FLOWER STRUCTURES EXAMPLES ANGULAR CHARACTERISTICS OF ?OW INVARIANT DOMAINS ADDITIONAL REMARKS