Contents 

Part 3     Global Behavior     331

	Mathematical Dynamics Hall of Fame     333

	10.  Global Phase Portraits     337
	     10.1  Multiple attractors     339
	     10.2  Actual and virtual separatrices     344

	11.  Generic Properties     349
	     11.1  Property G1 for critical points     351
	     11.2  Property G2 for closed orbits     354
	     11.3  Property G3 for saddle connections in 2D     357
	     11.4  Properties G4 and F     360

	12.  Structural Stability     363
	     12.1  Stability concepts     365
	     12.2  Peixoto's theorem     370
	     12.3  Peixoto's proof     374

	13.  Heteroclinic Tangles     377
	     13.1  Point to point     379
	     13.2  Outsets of the Lorenz mask     383
	     13.3  Point to cycle     391
	     13.4  Cycle to cycle     397
	     13.5  Birkhoff's signature     400

	14.  Homoclinic Tangles     407
	     14.1  Homoclinic cycles     409
	     14.2  Signature sequence     414
	     14.3  Horseshoes     420
	     14.4  Hypercycles     424

	15.  Nontrivial Recurrence     427
	     15.1  Nearly periodic orbits     429
	     15.2  Why Peixoto's theorem failed in 3D     436
	     15.3  Nonwandering Points     438