An International Workshop on Resonance Oscillations and Stability of Nonsmooth Systems has been held on June 16 – June 25, 2009 at Imperial College London, United Kingdom. There were 56 lectures and 4 posters presented by researchers from 17 countries that created a fruitful atmosphere for exploring the current research on resonance oscillations and stability of nonsmooth systems and understanding actual open problems coming from industrial applications. The organisers Oleg Makarenkov and Jeroen Lamb (Imperial College London) wish to thank the participants for their interest in the workshop that allowed it to be a success. Key speakers: Samir Adly (Limoges, France) Alain Jacquemard (Dijon, France) Marat Akhmet (Ankara, Turkey) Mike Jeffrey (Bristol, UK) Vladimir Babitsky (Loughborough, UK) Alexander Karapetyan (Moscow, Russia) Soumitro Banerjee (Kolkata, India) Tassilo Kupper (Koeln, Germany) Flaviano Battelli (Ancona, Italy) Ekaterina Pavlovskaia (Aberdeen, UK) Chris Budd (Bath, UK) Petri Piiroinen (Galway, Irland) David Chillingworth (Southampton, UK) Dmitrii Rachinskii (Cork, Ireland) Stephen Coombes (Nottingham, UK) Vladimir Ryabov (Hakodate, Japan) Gábor Csernák (Budapest, Hungary) Bruce Shaw (Columbia, USA) Alexander Fidlin (Karlsruhe, Germany) David Simpson (Colorado, USA) Damian Giaouris (Newcastle, UK) Marco Antonio Teixeira (Campinas, Brazil) Peter Giesl (Sussex, UK) Hans True (Lyngby, Denmark) John Hogan (Bristol, UK) Keith Worden (Sheffield, UK) Minisymposia: Current Mathematical Challenges in the Theory of Border Collision Bifurcations (19 June 2009) Organisers: Soumitro Banerjee (Kolkata, India) and Damian Giaouris (Newcastle, UK) Applications of Topological Degree to Study Nonsmooth Systems (23 June 2009) Organiser: Fabio Zanolin (Udine, Italy) Methods of Analysis of Systems with Hysteresis and Multi-scale systems (24 June 2009) Organiser: Dmitrii Rachinskii (Cork, Ireland) Generic singularities of nonsmooth systems: focusing on the 3D case and its consequences for dynamics (24 June 2009) Organisers: David Chillingworth (Southampton, UK) and Mike Jeffrey (Bristol, UK) Special sections : • Classification and normal forms for nonsmooth systems and maps • Theory of stability of nonsmooth systems • Resonance oscillations in nonsmooth systems with symmetry • Numerical bifurcation analysis of nonsmooth systems • Resonance oscillations in mechanical systems with elastic obstacles, dry friction or impacts • Open problems of nonsmooth bifurcation theory coming from control • Open mathematical problems and applications of nonsmooth bifurcation theory in engineering • Other topic Program, abstracts and presentations:

Group Photo (18th June 2009, 13:45) Speakers by countries        UK 17        Italy 7        USA 5        Russia 5        Ireland 4        Germany 3        Spain 2        Turkey 2        France 2        India 1        Brazil 1        Japan 1        Denmark 1        China 1        Hungary 1        Romania 1        Netherlands 1 Speakers by career stage Research students 5 Postdocs 5 Other young speakers 19 Session Coffee break

16 June 9:00-9:40 John Hogan (Bristol, UK) Nonsmooth systems: synchronization, sliding and other open problems abstract presentation:

17 June 9:00-9:40 Marat Akhmet (Ankara, Turkey) Stability of Differential Equations with Piecewise Constant Argument of Generalized Type abstract presentation:

18 June 9:00-9:40 Peter Giesl (Sussex, UK) Determination of the Basin of Attraction in periodic non-smooth systems abstract presentation:

19 June 9:00-9:40 Soumitro Banerjee (Kharagpu, India) The problem of singularity in impacting systems abstract presentation:

                 

16 June 9:45-10:25 Flaviano Battelli (Ancona, Italy) Chaos in discontinuous systems abstract presentation:

17 June 9:45-10:25 Samir Adly (Limoges, France) Nonsmooth Dynamical Systems: an overview abstract presentation:

18 June 9:45-10:25 Damian Giaouris (Newcastle, UK) Stability analysis of nonsmooth limit cycles abstract presentation:

19 June 9:45-10:25 David Simpson (Colorado, USA) Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps abstract presentation:

                 

16 June 10:55-11:35 Matteo Franca (Ancona, Italy) Persistence of homoclinic trajectory in discontinuous systems abstract presentation:

17 June 10:55-11:35 Alain Jacquemard (Dijon, France) Reversible and non-reversible non-smooth dynamical systems abstract presentation:

18 June 10:55-11:35 Gabor Csernak (Budapest, Hungary) Marginally stable asymmetric solutions of a dry friction oscillator abstract presentation:

19 June 10:55-11:35 Carolyn Berger (Durham, USA) Evidence for an Unfolded Border-Collision Bifurcation in Paced Cardiac Tissue abstract

                 

16 June 11:40-12:20 Alexander Karapetyan (Moscow, Russia) Generalized Smale Diagrams Approach to the Qualitative Analysis of the Dissipative Systems with Symmetries abstract presentation:

17 June 11:40-12:20 Mike Jeffrey (Bristol, UK) Invariant manifolds and nondeterministic dynamics around the Teixeira Singularity abstract presentation:

18 June 11:40-12:20 David Chillingworth (Southampton, UK) Phase space geometry for an impact oscillator near a degenerate graze abstract presentation:

19 June 11:40-12:20 Paul Glendinning (Manchester, UK) Unstable chaos, snap-back repellers and border collision bifurcations abstract presentation:

                 

16 June 13:50-14:30 Albert Granados (Stuttgart Germany) Bifurcations of feasible and virtual orbits in a ZAD-controlled buck converter abstract presentation:	17 June 13:50-14:30 Chris Budd (Bath, UK) Corner bifurcations, discontinuous maps and multiply impacting oscillators	18 June 13:50-14:30 Petri Piiroinen (Galway, Ireland) Global analysis of impacting systems abstract presentation:	19 June 13:50-14:30 Alan Champneys (Bristol, UK) Discontinuity mapping approach to computing "normal forms" for grazing bifurcations presentation:

                 

16 June 14:35-15:15 Vladimir Babitsky (Loughborough, UK) Excitation and control of nonsmooth resonant mode for ultrasonically assisted machining of intractable materials abstract

17 June 14:35-15:15 Alexander Fidlin (Karlsruhe, Germany) Effects of Dry Friction in Automotive Transmissions abstract

18 June 14:35-15:15 Ekaterina Pavlovskaia (Aberdeen, UK) Dynamics of impact oscillators with one sided motion constraint abstract

19 June 14:35-15:15 Tassilo Kupper (Köln, Germany) The reduction to invariant cones for nonsmooth systems abstract presentation:

                 

16 June 15:45-16:25 Stephen Coombes (Nottingham, UK) Gap junctions and emergent brain rhythms: A mathematical study abstract presentation:

17 June 15:45-16:25 Keith Worden (Sheffield, UK) Where Piecewise-Linear Systems Appear in Engineering Dynamics abstract presentation:

18 June 15:45-16:25 Vladimir Ryabov (Hokkaido, Japan) Non-smooth dynamics of friction in modeling of earthquakes abstract presentation:

19 June 15:45-16:25 Janos Turi (Dallas, USA) Critical Excitation for an Elasto-Plastic Oscillator abstract presentation:

                 

16 June 16:30-17:00 Neuroscience

17 June 16:30-17:00 Engineering

18 June 16:30-17:00 Earthquakes

19 June 16:30-17:00 Marco Antonio Teixeira (Campinas, Brazil) Stability of Non-smooth Systems abstract presentation:

                 

22 June 9:00-9:40 Qiang Zhang (Hong Kong, China) Anomalous phenomena in a simple nonsmooth system abstract

23 June 9:00-9:40 Walter Dambrosio (Torino, Italy) Planar Dirac systems in unbounded domains: the eigenvalue problem and a Maslov-type index abstract presentation:

24 June 9:00-9:30 Dmitrii Rachinskii (Cork, Ireland) Hysteresis loops generated by perturbation of systems with Devil's staircase nonlinearity abstract presentation:

25 June 9:00-9:40 Alexandra Zobova (Moscow, Russia) Analytical and Numerical Investigation of the double-spherical Tippe-Top Dynamics abstract presentation:

                 

22 June 9:45-10:25 Enrique Ponce (Sevilla, Spain) Unstable, continuous PWL differential systems whose all linear part are Hurwitz: two different examples abstract presentation:

23 June 9:40-10:20 Anna Capietto (Torino, Italy) Planar nonlinear Dirac systems: from the shooting method to global bifurcation abstract presentation:

24 June 9:30-10:00 Gary Friedman (Philadelphia, USA) Representation of Hysteresis with Return Point Memory: Expanding the Operator Basis abstract presentation:

25 June 9:45-10:25 Enes Yilmaz (Ankara, Turkey) Method of Lyapunov functions for differential equations with piecewise constant delay and its application to Neural networks model abstract presentation:

                 

22 June 10:25-11:00 Negative results abstract presentation:

23 June 11:00-11:50 Franco Obersnel (Trieste, Italy) First order periodic ODEs without uniqueness: complicated dynamics in simple problems abstract presentation:

24 June 10:00-10:30 Jan Sieber (Portsmouth, UK) Effect of singular perturbations on dynamical systems with sliding abstract presentation:

25 June 10:55-11:35 Mikhail Shunderyuk (Moscow, Russia) On nonlinear resonance oscillations of a spring supported point particle abstract

                 

22 June 13:30-14:10 Marcel Guardia (Barcelona, Spain) Codimension-2 singularities with infinitely many codimension-1 bifurcation branches abstract presentation:

23 June 11:50-12:40 Pierpaolo Omari (Trieste, Italia) Detecting stability and instability in periodic parabolic problems via lower and upper solutions abstract presentation:

24 June 11:10-11:40 Brian Appelbe (London, UK) An Investigation of Shape Memory Alloy Dynamics abstract

25 June 11:40-12:20 Benjamin Biemond (Eindhoven, The Netherlands ) A complete bifurcation analysis of planar conewise affine systems abstract presentation:

                 

22 June 14:15-14:55 Bruce Shaw (NY, USA) Complex Attractors in Wave Equations with Friction Compared with Earthquakes abstract presentation:

23 June 12:40-13:30 Fabio Zanolin (Udine, Italy) Complex dynamics in piecewise linear planar systems: a topological approach abstract presentation:

24 June 11:40-12:10 Nikola Popovic (Edinburgh, UK) Front Speeds, Cut-Offs, and the Blow-Up Method in Scalar Reaction-Diffusion Equations abstract presentation:

25 June 14:00-14:40 Piotr Kowalczyk (Manchester, UK) TBA presentation:

                 

22 June 15:35-16:15 Hans True (Kongens Lyngby, Denmark) Railway Vehicle Dynamics - a Challenge in Mathematics and Numerical Analysis abstract presentation:

23 June 15:00-15:40 Adriana Buica (Cluj-Napoca, Romania) Periodic solutions of the perturbed symmetric Euler top abstract presentation:

24 June 12:10-12:40 Hugh McNamara (Cork, Ireland) Modelling of macroeconomic and financial systems with hysteresis abstract presentation:

25 June 14:40-15:10 Classification of sliding bifurcations

                 

22 June 16:20-16:50 Railway vehicle dynamics

23 June 15:45-16:25 Maria Municina (Moscow, Russia) Two-cable System "Dumbbell-load" in Central Gravitational Field abstract presentation:

24 June 14:00-14:25 Marco Antonio Teixeira (Campinas - SP, Brazil) Symmetries and Bifurcation in Non-smooth Systems abstract presentation:

24 June 14 :45-15:05 Mike Jeffrey (Bristol, UK) Two-folds in Nonsmoth Dynamical Systems abstract presentation:

                 

Poster Valentin Tkhai (Moscow, Russia) Symmetric oscillations in non-smooth mechanical systems abstract

Poster Joanna Mason (Limerick, Ireland) Unfolding the dynamics of a nonsmooth model of gear rattle abstract

24 June 14:25-14:45 Alessandro Colombo (Milano, Italy) Invariant manifolds and nondeterministic dynamics around the Teixeira Singularity abstract presentation:

24 June 15:15-15:40 David Chillingworth (Southampton, UK) Robustness of Teixeira singularity dynamics and bifurcations abstract