To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.
Curriculum
teacher profile
teaching materials
Differentiable functions on a Banach space. The Implicit Function Theorem. Applications to the search of periodic solutions. Lyapunov Schmidt decomposition. Hopf theorem. Dependence on initial data. The flow box theorem. Coordinate changes generated by the flow of a vector field. The Lie exponential. Poincare normal form.
Chierchia Analisi Matematica 2
Mutuazione: 20410469 AM430 - EQUAZIONI DIFFERENZIALI ORDINARIE in Matematica LM-40 PROCESI MICHELA
Programme
Local existence and uniqueness theorems, existence times and extensions. Escape from compact sets. Comparison theorems. Behavior of linear systems with constant coefficients. Jordan canonical form.Differentiable functions on a Banach space. The Implicit Function Theorem. Applications to the search of periodic solutions. Lyapunov Schmidt decomposition. Hopf theorem. Dependence on initial data. The flow box theorem. Coordinate changes generated by the flow of a vector field. The Lie exponential. Poincare normal form.
Core Documentation
Note del docente.Chierchia Analisi Matematica 2
Type of delivery of the course
Lectures and exercisesType of evaluation
The written test consists of a series of exercises to be done at home. Then there is a colloquium on the topics of the course and the presentation of a dissertation.
teacher profile
teaching materials
Differentiable functions on a Banach space. The Implicit Function Theorem. Applications to the search of periodic solutions. Lyapunov Schmidt decomposition. Hopf theorem. Dependence on initial data. The flow box theorem. Coordinate changes generated by the flow of a vector field. The Lie exponential. Poincare normal form.
Chierchia Analisi Matematica 2
Mutuazione: 20410469 AM430 - EQUAZIONI DIFFERENZIALI ORDINARIE in Matematica LM-40 PROCESI MICHELA
Programme
Local existence and uniqueness theorems, existence times and extensions. Escape from compact sets. Comparison theorems. Behavior of linear systems with constant coefficients. Jordan canonical form.Differentiable functions on a Banach space. The Implicit Function Theorem. Applications to the search of periodic solutions. Lyapunov Schmidt decomposition. Hopf theorem. Dependence on initial data. The flow box theorem. Coordinate changes generated by the flow of a vector field. The Lie exponential. Poincare normal form.
Core Documentation
Note del docente.Chierchia Analisi Matematica 2
Type of delivery of the course
Lectures and exercisesType of evaluation
The written test consists of a series of exercises to be done at home. Then there is a colloquium on the topics of the course and the presentation of a dissertation.
teacher profile
teaching materials
Differentiable functions on a Banach space. The Implicit Function Theorem. Applications to the search of periodic solutions. Lyapunov Schmidt decomposition. Hopf theorem. Dependence on initial data. The flow box theorem. Coordinate changes generated by the flow of a vector field. The Lie exponential. Poincare normal form.
Chierchia Analisi Matematica 2
Mutuazione: 20410469 AM430 - EQUAZIONI DIFFERENZIALI ORDINARIE in Matematica LM-40 PROCESI MICHELA
Programme
Local existence and uniqueness theorems, existence times and extensions. Escape from compact sets. Comparison theorems. Behavior of linear systems with constant coefficients. Jordan canonical form.Differentiable functions on a Banach space. The Implicit Function Theorem. Applications to the search of periodic solutions. Lyapunov Schmidt decomposition. Hopf theorem. Dependence on initial data. The flow box theorem. Coordinate changes generated by the flow of a vector field. The Lie exponential. Poincare normal form.
Core Documentation
Note del docente.Chierchia Analisi Matematica 2
Type of delivery of the course
Lectures and exercisesType of evaluation
The written test consists of a series of exercises to be done at home. Then there is a colloquium on the topics of the course and the presentation of a dissertation.