definition 3.50 Identity map

Rests on

No declared or derived dependency edges point away from this node yet.

Supports

• depends_on definition 3.51 Inverse map ¶
  • depends_on definition 6.7 Homeomorphism ¶
    • depends_on definition 13.50 Diffeomorphism ¶
    • depends_on definition 13.53 Immersion, submersion, embedding ¶
      • depends_on definition 13.54 Embedded submanifold ¶
        • depends_on corollary 13.64 The image of a constant-rank map, locally ¶
        • depends_on definition 13.130 Distribution; involutive; integrable ¶
        • depends_on definition 13.58 Hypersurface ¶
        • depends_on proposition A.534 Every orbit is an embedded copy of $G$ ¶
        • depends_on theorem 13.67 Quotient manifold theorem ¶
        • depends_on theorem 13.62 Regular value theorem in codimension $k$ ¶
      • depends_on example 13.55 An injective immersion that is not an embedding ¶
      • depends_on lemma A.533 The orbit map has constant rank $d$ ¶
        • depends_on proposition A.534 Every orbit is an embedded copy of $G$ ¶ ↺
        • depends_on proposition A.535 Existence of a slice ¶
      • depends_on lemma A.538 Submersions have smooth local sections ¶
        • depends_on proposition A.539 Universal property ¶
      • depends_on proposition A.534 Every orbit is an embedded copy of $G$ ¶ ↺
      • depends_on theorem A.537 The smooth structure on the orbit space ¶
    • depends_on lemma A.536 A slice is a chart domain downstairs ¶
      • depends_on theorem A.537 The smooth structure on the orbit space ¶ ↺
    • depends_on theorem 32.15 Hartman–Grobman, restated from Part II ¶
      • depends_on definition 32.22 Bifurcation ¶
        • depends_on proposition 32.23 Saddle-node bifurcation ¶
        • depends_on proposition 32.24 Transcritical and pitchfork bifurcations ¶
        • depends_on theorem 32.25 Hopf bifurcation, quoted ¶
      • depends_on example 32.18 A linear centre that is really a stable focus ¶
    • depends_on theorem 9.32 Hartman–Grobman; quoted ¶
      • depends_on theorem 32.15 Hartman–Grobman, restated from Part II ¶ ↺
  • depends_on notation 4.13 The opposite map is not the inverse map ¶
  • depends_on proposition 3.63 prop:inf-equipotence-equivalence ¶
  • depends_on proposition 3.57 Composition of bijective maps ¶
    • depends_on proposition 3.63 prop:inf-equipotence-equivalence ¶ ↺
• depends_on proposition 3.63 prop:inf-equipotence-equivalence ¶ ↺
• depends_on proposition 3.56 Composition is associative ¶
  • depends_on proposition 3.57 Composition of bijective maps ¶ ↺