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Exponential map

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147: 95: 122: 17: 39: 132:, is sometimes also called the exponential map. The above two are special cases of this with respect to appropriate affine connections. 180: 45: 58: 24: 32: 16:
This page is about the exponential map in differential geometry. For discrete dynamical systems, see
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of mathematical analysis. Important special cases include:
163: 103: 61: 116: 89: 155:page lists articles associated with the title 138:forming the unit circle in the complex plane. 8: 18:Exponential map (discrete dynamical systems) 108: 102: 72: 60: 42:for a manifold with a Riemannian metric, 90:{\displaystyle X\mapsto \gamma _{X}(1)} 51:More generally, in a manifold with an 40:exponential map (Riemannian geometry) 7: 31:is a generalization of the ordinary 142:Topics referred to by the same term 48:from a Lie algebra to a Lie group, 14: 145: 84: 78: 65: 1: 46:exponential map (Lie theory) 117:{\displaystyle \gamma _{X}} 197: 144: 15: 128:with initial velocity 118: 91: 119: 92: 25:differential geometry 181:Disambiguation pages 101: 59: 33:exponential function 114: 87: 167: 53:affine connection 188: 161: 149: 123: 121: 120: 115: 113: 112: 96: 94: 93: 88: 77: 76: 196: 195: 191: 190: 189: 187: 186: 185: 171: 170: 169: 168: 160: 157:Exponential map 143: 136:Euler's formula 104: 99: 98: 68: 57: 56: 29:exponential map 21: 12: 11: 5: 194: 192: 184: 183: 173: 172: 153:disambiguation 150: 141: 140: 139: 133: 111: 107: 86: 83: 80: 75: 71: 67: 64: 49: 43: 13: 10: 9: 6: 4: 3: 2: 193: 182: 179: 178: 176: 165: 164:internal link 158: 154: 148: 137: 134: 131: 127: 109: 105: 81: 73: 69: 62: 54: 50: 47: 44: 41: 38: 37: 36: 34: 30: 26: 19: 156: 129: 28: 22: 106:γ 70:γ 66:↦ 175:Category 126:geodesic 97:, where 162:If an 27:, the 151:This 124:is a 23:In 177:: 55:, 159:. 130:X 110:X 85:) 82:1 79:( 74:X 63:X 20:.

Index

Exponential map (discrete dynamical systems)
differential geometry
exponential function
exponential map (Riemannian geometry)
exponential map (Lie theory)
affine connection
geodesic
Euler's formula
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disambiguation
internal link
Category
Disambiguation pages

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