Objective "Proposal Summary: While there have been tremendous advances in one-dimensional dynamics, higher-dimensional systems are far less well understood. This novel programme of work will take paradigms from one-dimensional dynamics to apply to the higher-dimensional case. In so doing, it will answer a number of long-standing questions of major significance and open up the field for sustained future investigation. The current emphasis on conformal (complex-analytic) techniques will be supplemented in the higher-dimensional setting by drawing on a combination of techniques from dynamics, geometry and analysis.• Take observations generated by a (possibly chaotic) dynamical system. Do their averages converge? Outcome A will show that for ‘typical’ one-dimensional systems this is indeed the case. This will solve a famous conjecture of Palis and that such maps are stochastically stable.• Outcome B will rule out certain pathologies in higher-dimensional systems with sufficient regularity. To do this, I will use the one-dimensional paradigm of rigidity associated to smoothness and build on work in progress to deal with the higher dimensionality.• Specifically, Poincare ́ asked whether recurrent orbits can be shadowed by periodic orbits for a system with nearby parameters. Outcome C will answer his question in a particular setting, using the one- dimensional paradigm of global deformations and higher-dimensional techniques.• Outcome D will give insight into dynamical systems associated to learning models in economics and game theory – concentrating on models that are either piecewise-affine, have time averages which are essentially piecewise affine, or can be viewed as stochastically perturbed systems. Systems associated to random graphs and coupled networks will also be investigated.The mathematical methods in these objectives are interlinked, and straddle pure and applied dynamics. This combined approach will greatly re-energise the field." Fields of science natural sciencesmathematicsapplied mathematicsdynamical systemsmedical and health sciencesbasic medicinepathologynatural sciencesmathematicsapplied mathematicsgame theorynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theory Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Call for proposal ERC-2013-ADG See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Host institution IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE EU contribution € 2 228 829,00 Address SOUTH KENSINGTON CAMPUS EXHIBITION ROAD SW7 2AZ LONDON United Kingdom See on map Region London Inner London — West Westminster Activity type Higher or Secondary Education Establishments Principal investigator Sebastian Van Strien (Prof.) Administrative Contact Brooke Alasya (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE United Kingdom EU contribution € 2 228 829,00 Address SOUTH KENSINGTON CAMPUS EXHIBITION ROAD SW7 2AZ LONDON See on map Region London Inner London — West Westminster Activity type Higher or Secondary Education Establishments Principal investigator Sebastian Van Strien (Prof.) Administrative Contact Brooke Alasya (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
