Symbolic Dynamics: Activity plan

Below is the current plan for all activities planned for the course. The meetings which are predominantly problem sessions are color coded blue. The meetings which are predominantly being used for project presentation are color coded pink. The remaining (white) meetings are lectures.

Sometimes, additional material or lecture notes can be made available here. Click on the date of the corresponding meeting to reach such material.

Day Subjects Primary material Secondary material

Sep 7 Welcome.
Formalities.
Introduction to symbolic dynamics.
Basic definitions and examples. LM 1.1-1.2 LM Preface Project catalog
Sep 8 Languages.
Higher block shifts.
Sliding block codes. LM 1.3-1.5 (except terms listed in next column) Details on periodicity (see Sep 29), irreducibility (see Sep 22), higher power shifts
Sep 14 Topology interrelation exercises I.
Exercises on fundamentals.
SupE 1-3, LME 1.2.3 LME 1.2.1-2, 1.2.4-5, LME 1.3.1-3
Sep 15 Sliding block codes, cont.
Shifts of finite type. LM 1.5, 2.1
Sep 21 Topology interrelation exercises II.
Exercises on SFT. SupE 4-6, LME 2.1.1 LME 2.1.2-3, 2.1.6, 2.1.9,
Sep 22 Graph shifts.
Graph representations.
State splitting LM 2.2-2.3 (except material in next column). LM 1.3.6. Details on higher power graphs. Description of Markov Chains (see Sep 28).
Sep 28 o Markov chains
Formal languages

Sep 29 State splitting.
Periodic points. LM 2.4.1-2.4.10 LM 1.1.3, 1.5.11, 6.3.1.
Oct 5 Exercises on SFT
LME 2.2.7, 2.2.9, 2.2.4, 2.4.5
Oct 6 State splitting by matrix.
Sofic shift basics. LM 2.4.11-2.4.14 LM 3.1-3.2.3
Oct 12 Data storage
SFT exercise LME 2.4.7
Oct 13
Symbolica
More about sofic shifts LM 3.2.4-3.2.10

Oct 19 Vacation
Oct 20 Vacation
Oct 26 Exercises on sofic shifts
LM 3.1.3, 3.2.2, 3.2.3, 3.2.4, 3.2.6
Oct 27 Uniqueness of sofic shift presentations
LM 3.3
Nov 2 Perron-Frobenius theory LM 4.2.2-4.2.3
Nov 3 When is a sofic shift an SFT?
Sofic shift algorithms.
Entropy basics
LM 4.1, 4.2.1, 3.4.17 LM 3.4.1-16, 3.4.18-19
Nov 9 Cancelled

Nov 10 Computing entropy
General dynamical systems LM 4.3, 4.4.1-5, 6.2, 6.3.2 LM 4.4.6-4.4.9, 4.5
Nov 16 Billard systems LM 6.5
Nov 17 Invariants.
Williams' theorem LM 6.4.1-6.4.7, 7.1.1-7.1.2 LM remainders of 6.3-4
Nov 23 Williams' theorem, continued
Strong shift equivalence (SSE) LM 7.1.3, 7.2.1
Nov 24 Shift equivalence vs SSE LM 7.2.2-7.2.12, 7.3.1
Nov 30 Entropy and classification exercises LME 4.1.2, 4.1.5(c)(d), 4.3.4, 6.3.1(a)(b), 7.2.1, 7.2.2
Dec 1 Interpretation of SSE LM 7.5
Shift equivalence invariants LM 7.4
Dec 7 Cancelled
Dec 8 Shift equivalence invariants LM Remainder of 7.4
Dec 14 Cancelled
Dec 15 Cancelled

Day	Subjects	Primary material	Secondary material
Sep 7	Welcome. Formalities. Introduction to symbolic dynamics. Basic definitions and examples.	LM 1.1-1.2	LM Preface Project catalog
Sep 8	Languages. Higher block shifts. Sliding block codes.	LM 1.3-1.5 (except terms listed in next column)	Details on periodicity (see Sep 29), irreducibility (see Sep 22), higher power shifts
Sep 14	Topology interrelation exercises I. Exercises on fundamentals.	SupE 1-3, LME 1.2.3	LME 1.2.1-2, 1.2.4-5, LME 1.3.1-3
Sep 15	Sliding block codes, cont. Shifts of finite type.	LM 1.5, 2.1
Sep 21	Topology interrelation exercises II. Exercises on SFT.	SupE 4-6, LME 2.1.1	LME 2.1.2-3, 2.1.6, 2.1.9,
Sep 22	Graph shifts. Graph representations. State splitting	LM 2.2-2.3 (except material in next column). LM 1.3.6.	Details on higher power graphs. Description of Markov Chains (see Sep 28).
Sep 28 o	Markov chains Formal languages
Sep 29	State splitting. Periodic points.	LM 2.4.1-2.4.10 LM 1.1.3, 1.5.11, 6.3.1.
Oct 5	Exercises on SFT	LME 2.2.7, 2.2.9, 2.2.4, 2.4.5
Oct 6	State splitting by matrix. Sofic shift basics.	LM 2.4.11-2.4.14 LM 3.1-3.2.3
Oct 12	Data storage
SFT exercise	LME 2.4.7
Oct 13	Symbolica
More about sofic shifts	LM 3.2.4-3.2.10
Oct 19	Vacation
Oct 20	Vacation
Oct 26	Exercises on sofic shifts	LM 3.1.3, 3.2.2, 3.2.3, 3.2.4, 3.2.6
Oct 27	Uniqueness of sofic shift presentations	LM 3.3
Nov 2	Perron-Frobenius theory	LM 4.2.2-4.2.3
Nov 3	When is a sofic shift an SFT? Sofic shift algorithms. Entropy basics	LM 4.1, 4.2.1, 3.4.17	LM 3.4.1-16, 3.4.18-19
Nov 9	Cancelled
Nov 10	Computing entropy General dynamical systems	LM 4.3, 4.4.1-5, 6.2, 6.3.2	LM 4.4.6-4.4.9, 4.5
Nov 16	Billard systems		LM 6.5
Nov 17	Invariants. Williams' theorem	LM 6.4.1-6.4.7, 7.1.1-7.1.2	LM remainders of 6.3-4
Nov 23	Williams' theorem, continued Strong shift equivalence (SSE)	LM 7.1.3, 7.2.1
Nov 24	Shift equivalence vs SSE	LM 7.2.2-7.2.12, 7.3.1
Nov 30	Entropy and classification exercises	LME 4.1.2, 4.1.5(c)(d), 4.3.4, 6.3.1(a)(b), 7.2.1, 7.2.2
Dec 1	Interpretation of SSE		LM 7.5
Shift equivalence invariants	LM 7.4
Dec 7	Cancelled
Dec 8	Shift equivalence invariants	LM Remainder of 7.4
Dec 14	Cancelled
Dec 15	Cancelled

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