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Rigidity and global deformations in dynamics

"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 a... ver más

28/02/2019

IMPERIAL COLLEGE O...

2M€

Presupuesto del proyecto: 2M€

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IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND ME... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2019-02-28 No tenemos la información de la convocatoria

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IMPERIAL COLLEGE OF SCIENCE...

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Líder del proyecto

IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND ME... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 2M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto "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."

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