I don't think there is any rigorous mathematical definition of dynamic, or to phrase it better, the definition is embedded in the definition of dynamical system itself (which would be probably a better term to use in place of the generic "sequence"):

A dynamical system is formally defined as a state space $X$, a set of time points $T$, and a rule $R$ that specifies how the state evolves with time. The rule $R$ is a function whose domain is $X×T$ and whose codomain is $X$, i.e., $R:X×T→X$. The rule function $R$ means that the $R$ takes two inputs, $R=R(x,t)$, where $x∈X$ is the initial state (at time $t=0$, for example) and $t∈T$ is a future time. In other words, $R(x,t)$ gives the state at time t given that the initial state was $x$.

I think that what the paragraph states is that we assume the rule funcion R to remain the same, cause that's what we're trying to learn.

As a final note, there are out there also classifications of different non-linear dynamical systems, based on the property of $R$.

I don't think there is any rigorous mathematical definition of dynamic, or to phrase it better, the definition is embedded in the definition of dynamical system itself (which would be probably a better term to use in place of the generic "sequence"):

A dynamical system is formally defined as a state space $X$, a set of time points $T$, and a rule $R$ that specifies how the state evolves with time. The rule $R$ is a function whose domain is $X×T$ and whose codomain is $X$, i.e., $R:X×T→X$. The rule function $R$ means that the $R$ takes two inputs, $R=R(x,t)$, where $x∈X$ is an initial state and $t∈T$ is a specific time step.

I think that what the paragraph states is that we assume the rule funcion R to remain the same, cause that's what we're trying to learn.

As a final note, there are out there also classifications of different non-linear dynamical systems, based on the property of $R$.

I don't think there is any rigorous mathematical definition of dynamic, or to phrase it better, the definition is embedded in the definition of dynamical system itself:

A dynamical system is formally defined as a state space $X$, a set of time points $T$, and a rule $R$ that specifies how the state evolves with time. The rule $R$ is a function whose domain is $X×T$ and whose codomain is $X$, i.e., $R:X×T→X$. The rule function $R$ means that the $R$ takes two inputs, $R=R(x,t)$, where $x∈X$ is the initial state (at time $t=0$, for example) and $t∈T$ is a future time. In other words, $R(x,t)$ gives the state at time t given that the initial state was $x$.

I think that what the paragraph states is that we assume the rule funcion R to remain the same, cause that's what we're trying to learn.

As a final note, there are out there also classifications of different non-linear dynamical systems, based on the property of $R$.

I don't think there is any rigorous mathematical definition of dynamic, or to phrase it better, the definition is embedded in the definition of dynamical system itself (which would be probably a better term to use in place of the generic "sequence"):

A dynamical system is formally defined as a state space $X$, a set of time points $T$, and a rule $R$ that specifies how the state evolves with time. The rule $R$ is a function whose domain is $X×T$ and whose codomain is $X$, i.e., $R:X×T→X$. The rule function $R$ means that the $R$ takes two inputs, $R=R(x,t)$, where $x∈X$ is the initial state (at time $t=0$, for example) and $t∈T$ is a future time. In other words, $R(x,t)$ gives the state at time t given that the initial state was $x$.

I think that what the paragraph states is that we assume the rule funcion R to remain the same, cause that's what we're trying to learn.

As a final note, there are out there also classifications of different non-linear dynamical systems, based on the property of $R$.