## Complex Polynomial Vector Fields

Research output: Non-textual form › Sound/Visual production (digital) – Annual report year: 2007 › Research

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**Complex Polynomial Vector Fields.**Dias, Kealey (Author). 2007. Event: 11th Danish Center for Applied Mathematics and Mechanics, SAS Radisson Hotel, Silkeborg, Denmark.

Research output: Non-textual form › Sound/Visual production (digital) – Annual report year: 2007 › Research

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*Complex Polynomial Vector Fields*, 2007, Sound/Visual production (digital).

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*Complex Polynomial Vector Fields*, Sound/Visual production (digital), 2007, 11th Danish Center for Applied Mathematics and Mechanics, Silkeborg, 19 Mar 2007

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### RIS

TY - ADVS

T1 - Complex Polynomial Vector Fields

A2 - Dias, Kealey

PY - 2007

Y1 - 2007

N2 - The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.

AB - The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.

KW - Holomorphic

M3 - Sound/Visual production (digital)

ER -