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CRM > English > Activities > Curs 2015-2016 > Advanced Course on Piecewise Smooth Dynamical Systems
Advanced Course on Piecewise Smooth Dynamical Systems

SCHEDULE

 

Monday, April 11

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08:45-09:00

​​Registration and badge pick up

09:00-09:50

Introduction to the dynamics of piecewise smooth flows (I)

Mike Jeffrey (University of Bristol)

09:50-10:00

Discussion/Break

10:00-10:50

Introduction to the dynamics of piecewise smooth flows (II)

Mike Jeffrey (University of Bristol)

10:50-11:00

Discussion/Break

11:00-11:30

Coffee break

11:30-12:20

Introduction to the dynamics of piecewise smooth maps (I)

Paul Glendinning (University of Manchester)

12:20-12:30

Discussion/Break

12:30-13:20

Introduction to the dynamics of piecewise smooth maps (II)

Paul Glendinning (University of Manchester)

13:20-13:30

Discussion/Break

13:30-15:00

Lunch break

15:00-15:50

Guest lecture: 

Sustainable Development Olivar_Gerard.pdfAbstract

Gerard Olivar (Universidad Nacional de Colombia)

15:50-16:10

Discussion/Break

16:10-17:00

Problem class

17:00-17:10

Discussion/Break

 

Tuesday, April 12

​​

09:00-09:50

Introduction to the dynamics of piecewise smooth maps (III)

Paul Glendinning (University of Manchester)

09:50-10:00

Discussion/Break

10:00-10:50

Introduction to the dynamics of piecewise smooth maps (IV)

Paul Glendinning (University of Manchester)

10:50-11:00

Discussion/Break

11:00-11:30

Coffee break

11:30-12:20

Introduction to the dynamics of piecewise smooth flows (III)

Mike Jeffrey (University of Bristol)

12:20-12:30

Discussion/Break

12:30-13:20

Introduction to the dynamics of piecewise smooth flows (IV)

Mike Jeffrey (University of Bristol)

13:20-13:30

Discussion/Break

13:30-15:00

Lunch break

15:00-15:50

Guest lecture: 

Sliding-Mode Control and Stability Analysis of DC-DC Switching Converters ElAroudi_Abdelali.pdfAbstract

Abdelali El Aroudi (Universitat Rovira i Virgili)

15:50-16:10

Discussion/Break

16:10-17:00

Problem class

17:00-17:10

Discussion/Break

 

Wednesday, April 13

09:00-09:50

Introduction to the dynamics of piecewise smooth flows (V)

Mike Jeffrey (University of Bristol)

09:50-10:00

Discussion/Break

10:00-10:50

Introduction to the dynamics of piecewise smooth flows (VI)

Mike Jeffrey (University of Bristol)

10:50-11:00

Discussion/Break

11:00-11:30

Coffee break

11:30-12:20

Introduction to the dynamics of piecewise smooth maps (V)

Paul Glendinning (University of Manchester)

12:20-12:30

Discussion/Break

12:30-13:20

Introduction to the dynamics of piecewise smooth maps (VI)

Paul Glendinning (University of Manchester)

13:20-13:30

Discussion/Break

13:30-15:00

Lunch break

15:00-15:50

Guest lecture:

Characterizing the compound bifurcation in the Teixeira singularity for piecewise linear systems Ponce_Enrique.pdfAbstract.pdf

Enrique Ponce (Universidad de Sevilla)

15:50-16:10

Discussion/Break

16:10-17:00

Problem class

17:00-17:10

Discussion/Break

 

Thursday, April 14

09:00-09:50

Introduction to the dynamics of piecewise smooth maps (VII)

Paul Glendinning (University of Manchester)

09:50-10:00

​Discussion/Break

10:00-10:50

Introduction to the dynamics of piecewise smooth maps (VIII)

Paul Glendinning (University of Manchester)

10:50-11:00

Discussion/Break

11:00-11:30

Coffee break

11:30-12:20

Introduction to the dynamics of piecewise smooth flows (VII)

Mike Jeffrey (University of Bristol)

12:20-12:30

Discussion/Break

12:30-13:20

Introduction to the dynamics of piecewise smooth flows (VIII)

Mike Jeffrey (University of Bristol)

13:20-13:30

Discussion/Break

13:30-15:00

Lunch break

Guided visit (more information to be sent to the participants)

Dinner (more information to be sent to the participants)

 

Friday, April 15

09:0​0-09:50

Introduction to the dynamics of piecewise smooth flows (IX)

Mike Jeffrey (University of Bristol)

09:50-10:00

Discussion/Break

10:00-10:50

Introduction to the dynamics of piecewise smooth flows (X)

Mike Jeffrey (University of Bristol)

10:50-11:00

Discussion/Break

11:00-11:30

Coffee break

11:30-12:20

Introduction to the dynamics of piecewise smooth maps (IX)

Paul Glendinning (University of Manchester)

12:20-12:30

Discussion/Break

12:30-13:20

Introduction to the dynamics of piecewise smooth maps (X)

Paul Glendinning (University of Manchester)

13:20-13:30

Discussion/Break

13:30-15:00

Lunch break

15:00-15:50

Guest lecture: 

Analytic computation of periodic solutions of piecewise differential systems  Llibre_Jaume.pdfAbstract

Jaume Llibre (Universitat Autònoma de Barcelona)

15:50-16:10

Discussion/Break

16:10-17:00

Problem class

17:00-17:10

Discussion/Break

 


The Course:

Part 1. Introduction to the dynamics of piecewise smooth maps, by Paul Glendinning (University of Manchester)

  • Phenomenology of piecewise smooth systems and some techniques from smooth theory. Basic stability analysis.
  • Piecewise Monotonic Maps of the Interval:
  • Examples and bifurcation diagrams, boundary bifurcations, transitivity.
  • Rotation-like maps, gluing bifurcations (aka Big Bang Bifurcations and period-adding), an introduction to renormalization.
  • Decomposition Theorems and a brief guide to kneading theory.
  • Piecewise Smooth maps of the plane:
    Lozi and the border collision normal form, piecewise isometries (phenomenology and early results). Bounding regions.
  • Periodic orbits and resonance.
  • Robust chaos. Two-dimensional attractors.
  • Challenges in Higher Dimensions:
  • Periodic orbits (Feigen), N-dimensional attractors, analogies with smooth cases.

Part 2. Introduction to the dynamics of piecewise smooth flows, by Mike Jeffrey (University of Bristol)

  • History & Applications
  • Inclusions vs. Combinations
  • Crossing and Sliding
  • Switching layers
  • Layer variables
  • Multiple switches
  • Switching layers
  • Discontinuity-induced phenomena
  • Determinacy breaking
  • Stability, equivalence, & bifurcation
  • Singularities in the plane

 

Part 3. Alongside the main lectures there will be guest lectures focussed on applications, and time for problem solving. The students will have singular access to all of the resident members of the Intensive Research Program on Advances in Nonsmooth Dynamics running throughout February-April at the CRM.


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