Math 635: Dynamical Systems - Revision history

Ls5: moved Math 635 to Math 635: Dynamical Systems

2013-04-03T22:44:11Z

2010-07-28T16:36:23Z

‎Minimal learning outcomes

2009-06-04T19:20:25Z

2009-02-26T23:05:24Z

2008-08-28T21:33:22Z

‎Description

2008-08-12T22:22:53Z

‎Minimal learning outcomes

2008-08-12T22:22:13Z

‎Desired Learning Outcomes

2008-08-12T22:20:49Z

‎Minimal learning outcomes

2008-08-12T22:20:25Z

‎Minimal learning outcomes

2008-08-12T22:19:09Z

‎Additional topics

@@ Line 22: / Line 22: @@
 === Minimal learning outcomes ===
 Students should achieve mastery of the topics
 below. This means that they should know all relevant definitions,
@@ Line 34: / Line 29: @@
 given by the instructor.
 #	Topological dynamical systems
 #*	Nonwandering set, chain recurrence
@@ Line 43: / Line 40: @@
 #*	Subshifts of finite type
 #*	Perron-Frobenius theorem
-#*	Topological entropy for subshifts of finite type
+#*	Topological entropy for subshifts of finite type<br><br><br>
 #	Hyperbolic dynamical systems
 #*	Hartman-Grobman theorem
@@ Line 56: / Line 53: @@
 #*	Real quadratic maps
 #*	Expanding endomorphisms
 === Additional topics ===

@@ Line 11: / Line 11: @@
 === Description ===
+(A rigorous treatment of the theory of dynamical systems.?)
 A rigorous treatment of the theory of dynamical systems.
 == Desired Learning Outcomes ==
@@ Line 67: / Line 66: @@
 === Courses for which this course is prerequisite ===
 [[Category:Courses|635]]

← Older revision		Revision as of 23:05, 26 February 2009
Line 61:		Line 61:

	These are at the instructor's discretion as time allows examples are: Ergodic theory, Markov partitions, Sharkovsky theorem, Hamiltonian dynamics, and measure theoretic entropy.		These are at the instructor's discretion as time allows examples are: Ergodic theory, Markov partitions, Sharkovsky theorem, Hamiltonian dynamics, and measure theoretic entropy.
		+
		+	=== Recommended texts ===
		+
		+	Dynamical Systems, stability, symbolic dynamics, and chaos, by Clark Robinson; Introduction to Dynamical Systems, by Michael Brin and Garrett Stuck

	=== Courses for which this course is prerequisite ===		=== Courses for which this course is prerequisite ===

@@ Line 12: / Line 12: @@
 === Description ===
-This course is designed to provide students with a rigorous treatment of the theory of dynamical systems.
+A rigorous treatment of the theory of dynamical systems.
 == Desired Learning Outcomes ==

@@ Line 43: / Line 43: @@
 #	Symbolic dynamical systems
 #*	Subshifts of finite type
-#*	Perron-Frobenius Theorem
+#*	Perron-Frobenius theorem
 #*	Topological entropy for subshifts of finite type
 #	Hyperbolic dynamical systems

← Older revision	Revision as of 22:44, 3 April 2013
(No difference)

@@ Line 24: / Line 24: @@
 </div>
-: Students should achieve mastery of the topics
+Students should achieve mastery of the topics
 below. This means that they should know all relevant definitions,
 full statements of the major theorems, and examples of the various

← Older revision		Revision as of 22:20, 12 August 2008
Line 23:		Line 23:

	</div>		</div>
		+
		+	: Students should achieve mastery of the topics
		+	below. This means that they should know all relevant definitions,
		+	full statements of the major theorems, and examples of the various
		+	concepts. Further, students should be able to solve non-trivial problems
		+	related to these concepts, and prove theorems in analogy to proofs
		+	given by the instructor.
		+
		+	# Topological dynamical systems
		+	#* Nonwandering set, chain recurrence
		+	#* Topological mixing and transitivity
		+	#* Expansive systems
		+	#* Topological entropy
		+	#* Topological and smooth conjugacy
		+	# Symbolic dynamical systems
		+	#* Subshifts of finite type
		+	#* Perron-Frobenius Theorem
		+	#* Topological entropy for subshifts of finite type
		+	# Hyperbolic dynamical systems
		+	#* Hartman-Grobman theorem
		+	#* Stable manifold theorem
		+	#* Hyperbolic sets
		+	#* Anosov diffeomorphisms
		+	#* Smale Horseshoe and transverse homoclinic points
		+	#* Shadowing
		+	#* Axiom A dynamical systems and spectral decomposition
		+	# Low dimensional dynamical systems
		+	#* Circle homeomorphisms, circle diffeomorphisms, and rotation number
		+	#* Real quadratic maps
		+	#* Expanding endomorphisms

	=== Additional topics ===		=== Additional topics ===

@@ Line 26: / Line 26: @@
 === Additional topics ===
-These are at the instructor's discretion as time allows examples are: Ergodic theory, Markov partitions, Sharkovsky theorem, Hamiltonian dynamics and measure theoretic entropy.
+These are at the instructor's discretion as time allows examples are: Ergodic theory, Markov partitions, Sharkovsky theorem, Hamiltonian dynamics, and measure theoretic entropy.
 === Courses for which this course is prerequisite ===