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1 = Introduction to dynamical systems and chaotic systems, fall 2015 =
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5 {{panel}}
6 **Teacher:** [[Paolo Muratore-Ginanneschi>>doc:mathstatHenkilokunta.Muratore-Ginanneschi, Paolo]], [[Kay Schwieger>>url:http://Kay Schwieger||shape="rect"]]
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8 **Scope:** 10 cr
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10 **Type:** Advanced studies
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12 **Teaching:**
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14 **Topics:**
15
16 **Prerequisites:**
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18
19 === {{toc maxLevel="4" minLevel="2" indent="20px"/}} ===
20
21 == News ==
22
23 * 11.09: the course has now a dedicated [[presemo room>>url:http://presemo.helsinki.fi/introdynsys||shape="rect"]].
24 Presemo is a web space which students can use to post questions, comments or simply to discuss about the course. Teachers will check the room weekly. It must not be therefore used for asking urgent questions to the teachers. We will also try to use the [[presemo room>>url:http://presemo.helsinki.fi/introdynsys||shape="rect"]] during the lectures for checking the student response to multi-answer questions. Postings and responses are anonymous. In no case they or any other civilized activity will be used for grading. In order to use the [[presemo room>>url:https://wiki.helsinki.fi/h||shape="rect"]], just follow the link.
25 * (% style="color: rgb(128,0,0);" %)EXAM: on Thursday 10.12.2015  in DK116 from 10:00 to 14:00
26 * (% style="color: rgb(128, 0, 0); color: rgb(128, 0, 0)" %)EXAM: on Friday 29.01.2016  in C129 from 13:00 to 17:00
27
28 == Teaching schedule ==
29
30 Weeks 36-42 and 44-50, Monday and Friday 14-16 in room C124.
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32 (% style="color: rgb(128,0,0);" %)First Lecture: Friday 04.09
33
34 == Exams ==
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36
37
38 == Course material ==
39
40 The course will be based on:
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42 * Steven H. Strogatz: //[[Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering>>url:http://www.stevenstrogatz.com/books/nonlinear-dynamics-and-chaos-with-applications-to-physics-biology-chemistry-and-engineering||shape="rect"]] //. Westview Press Classroom Classics (2014).
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44 There exists a huge literature on dynamical systems. Among them I can recommend
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46 * M.W. Hirsch, S. Smale, R. Devaney: //[[Differential Equations, Dynamical Systems and an Introduction to Chaos>>url:http://www.sciencedirect.com/science/book/9780123820105||rel="nofollow" shape="rect" class="external link"]]//. Elsevier (2013)
47 * Massimo Cencini, Fabio Cecconi and Angelo Vulpiani[[: // Chaos: From Simple Models to Complex Systems//>>url:http://denali.phys.uniroma1.it/%7EchaosbookCCV09/Site/%22Chaos%3A_from_simple_models_to_complex_systems%22_companion_site.html||rel="nofollow" shape="rect" class="external-link"]]. World Scientific(2009)
48 * Pierre Collet and Jean-Pierre Eckmann~:// [[Concepts and Results in Chaotic Dynamics>>url:http://books.google.fi/books/about/Concepts_and_Results_in_Chaotic_Dynamics.html?id=HopJYk7RmMQC&redir_esc=y||rel="nofollow" shape="rect" class="external-link"]]// Springer Science & Business Media (2006)
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50 Useful lecture notes are
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52 * //[[Geometrical theory of dynamical systems>>url:http://arxiv.org/abs/math.HO/0111177||rel="nofollow" shape="rect" class="external-link"]]//, Nils Berglund (2001),
53 * //[[Perturbation theory of dynamical systems>>url:http://arxiv.org/abs/math.HO/0111178||rel="nofollow" shape="rect" class="external-link"]]//, Nils Berglund (2001)
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55 which can be freely downloaded from [[arXiv.org>>url:http://arxiv.org/||rel="nofollow" shape="rect" class="external-link"]].
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57 Finally, Strogatz has posted on YouTube videos of his Cornell lectures:
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59 (% class="pl-header-title" %)
60 [[Nonlinear Dynamics and Chaos>>url:https://www.youtube.com/playlist?list=PLbN57C5Zdl6j_qJA-pARJnKsmROzPnO9V||shape="rect"]] - Steven Strogatz, Cornell University.
61
62 == Presemo ==
63
64 The course as a dedicated [[presemo room>>url:http://presemo.helsinki.fi/introdynsys||shape="rect"]] (web space). To access this web space just follow the foregoing link.  Students are encouraged to use the [[presemo room>>url:http://presemo.helsinki.fi/introdynsys||shape="rect"]] for any civilized activity pertaining the course. We will also try to use the [[presemo room>>url:http://presemo.helsinki.fi/introdynsys||shape="rect"]] during the lectures for checking the student response to multi-answer questions. For this reason, we encourage students to have a mobile device with them when attending classes.
65
66 == Registration ==
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68
69 (% style="color: rgb(96,96,96);" %)Did you forget to register?(%%) (% style="color: rgb(96,96,96);" %) (%%) [[What to do?>>url:https://wiki.helsinki.fi/display/mathstatOpiskelu/Kysymys4||style="text-decoration: underline;" shape="rect"]]
70
71 == Lecture Notes ==
72
73 * [[Binary shift map>>attach:binary_shift_map.pdf]]
74 * [[Normal Forms>>attach:normal_forms.pdf]]
75
76 == Exercises ==
77
78 === Assignments ===
79
80 * [[Sheet 1>>attach:Exercise_1.pdf]]
81 * [[Sheet 2>>attach:Exercise_2.pdf]]
82 * [[Sheet 3>>attach:Exercise_3.pdf]]
83 * [[Sheet 4>>attach:Exercise_4.pdf]]
84 * [[Sheet 5>>attach:Exercise_5.pdf]]
85 * [[Sheet 6>>attach:Exercise_6.pdf]]
86 * [[Sheet 7>>attach:Exercise_7.pdf]]
87 * [[Sheet 8>>attach:Exercise_8.pdf]]
88 * [[Sheet 9>>attach:Exercise_9.pdf]]
89 * [[Sheet 10>>attach:Exercise_10.pdf]]
90 * [[Sheet 11>>attach:Exercise_11.pdf]]
91 * In the exercise session on Fr., Dec. 4, we are going to review and summarize all previous exercise sheets.
92
93 === Exercise classes ===
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95 |=(((
96 Group
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98 Day
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100 Time
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102 Room
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104 Instructor
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107 1.
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109 Friday
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111 13-14
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113 C123
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115 Kay Schwieger
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117
118 == Course feedback ==
119
120 Course feedback can be given at any point during the course. Click [[here>>url:https://elomake.helsinki.fi/lomakkeet/11954/lomake.html||style="line-height: 1.4285;" shape="rect"]].