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user7807
user7807

I have seen talks about this, though somewhat over my head. But, yes absolutely, people do research such things. A. Katok is one name that comes to mind here. See this paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.2082

They consider actions of $\mathbb{Z}^k$ and $\mathbb{R}^k$ that generalize the usual time-like case of $\mathbb{Z}$ and $\mathbb{R}$.

B. Kalinin and V. Sadovskaya also work in this area, seeing their talks was how I was exposed to this field: http://www.southalabama.edu/mathstat/personal_pages/sadovska/Research/tns.pdf

A lot of the work I've been exposed to is about classifying such systems up to a conjugacy, and in particular they consider Anosov systems and see if they can find conjugacies in the general case to canonical exampleexamples.

This is not my expertise, though, so I can't say what this says about the $\mathbb{C}$ case you're interested in. But at least I can say, yes, indeed there is work in the higher-dimensional case.

I have seen talks about this, though somewhat over my head. But, yes absolutely, people do research such things. A. Katok is one name that comes to mind here. See this paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.2082

They consider actions of $\mathbb{Z}^k$ and $\mathbb{R}^k$ that generalize the usual time-like case of $\mathbb{Z}$ and $\mathbb{R}$.

B. Kalinin and V. Sadovskaya also work in this area, seeing their talks was how I was exposed to this field: http://www.southalabama.edu/mathstat/personal_pages/sadovska/Research/tns.pdf

A lot of the work I've been exposed to is about classifying such systems up to a conjugacy, and in particular they consider Anosov systems and see if they can find conjugacies in the general case to canonical example.

This is not my expertise, though, so I can't say what this says about the $\mathbb{C}$ case you're interested in. But at least I can say, yes, indeed there is work in the higher-dimensional case.

I have seen talks about this, though somewhat over my head. But, yes absolutely, people do research such things. A. Katok is one name that comes to mind here. See this paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.2082

They consider actions of $\mathbb{Z}^k$ and $\mathbb{R}^k$ that generalize the usual time-like case of $\mathbb{Z}$ and $\mathbb{R}$.

B. Kalinin and V. Sadovskaya also work in this area, seeing their talks was how I was exposed to this field: http://www.southalabama.edu/mathstat/personal_pages/sadovska/Research/tns.pdf

A lot of the work I've been exposed to is about classifying such systems up to a conjugacy, and in particular they consider Anosov systems and see if they can find conjugacies in the general case to canonical examples.

This is not my expertise, though, so I can't say what this says about the $\mathbb{C}$ case you're interested in. But at least I can say, yes, indeed there is work in the higher-dimensional case.

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Source Link
user7807
user7807

I have seen talks about this, though somewhat over my head. But, yes absolutely, people do research such things. A. Katok is one name that comes to mind here. See this paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.2082

They consider actions of $\mathbb{Z}^k$ and $\mathbb{R}^k$ that generalize the usual time-like case of $\mathbb{Z}$ and $\mathbb{R}$.

B. Kalinin and V. Sadovskaya also work in this area, seeing their talks was how I was exposed to this field: http://www.southalabama.edu/mathstat/personal_pages/sadovska/Research/tns.pdf

A lot of the work I've been exposed to is about classifying such systems up to a conjugacy, and in particular they consider Anosov systems and see if they can find conjugacies in the general case to canonical example.

This is not my expertise, though, so I can't say what this says about the $\mathbb{C}$ case you're interested in. But at least I can say, yes, indeed there is work in the higher-dimensional case.

I have seen talks about this, though somewhat over my head. But, yes absolutely, people do research such things. A. Katok is one name that comes to mind here. See this paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.2082

They consider actions of $\mathbb{Z}^k$ and $\mathbb{R}^k$ that generalize the usual time-like case of $\mathbb{Z}$ and $\mathbb{R}$.

This is not my expertise, though, so I can't say what this says about the $\mathbb{C}$ case you're interested in. But at least I can say, yes, there is work in the higher-dimensional case.

I have seen talks about this, though somewhat over my head. But, yes absolutely, people do research such things. A. Katok is one name that comes to mind here. See this paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.2082

They consider actions of $\mathbb{Z}^k$ and $\mathbb{R}^k$ that generalize the usual time-like case of $\mathbb{Z}$ and $\mathbb{R}$.

B. Kalinin and V. Sadovskaya also work in this area, seeing their talks was how I was exposed to this field: http://www.southalabama.edu/mathstat/personal_pages/sadovska/Research/tns.pdf

A lot of the work I've been exposed to is about classifying such systems up to a conjugacy, and in particular they consider Anosov systems and see if they can find conjugacies in the general case to canonical example.

This is not my expertise, though, so I can't say what this says about the $\mathbb{C}$ case you're interested in. But at least I can say, yes, indeed there is work in the higher-dimensional case.

Source Link
user7807
user7807

I have seen talks about this, though somewhat over my head. But, yes absolutely, people do research such things. A. Katok is one name that comes to mind here. See this paper: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.2082

They consider actions of $\mathbb{Z}^k$ and $\mathbb{R}^k$ that generalize the usual time-like case of $\mathbb{Z}$ and $\mathbb{R}$.

This is not my expertise, though, so I can't say what this says about the $\mathbb{C}$ case you're interested in. But at least I can say, yes, there is work in the higher-dimensional case.