Above are papers related to the following paper: [Paper_ID] Paper #121792. 	[Title] DISCRETE-TIME TRANSITIVITY AND ACCESSIBILITY: ANALYTIC SYSTEMS 1 [Abstract] This paper studies the problem, and establishes the desired implication for analytic systems in several cases: (i) compact state space, (ii) under a Poisson stability condition, and (iii) in a generic sense. In addition, the paper studies accessibility properties of the "control sets" recently introduced in the context of dynamical systems studies. Finally, various examples and counterexamples are provided relating the various Lie algebras introduced in past work. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152394. 	[Title]  [Abstract] FURTHER RESULTS ON CONTROLLABILITY PROPERTIES OF DISCRETE-TIME NONLINEAR SYSTEMS fl ABSTRACT Controllability questions for discrete-time nonlinear systems are addressed in this paper. In particular, we continue the search for conditions under which the group-like notion of transitivity implies the stronger and semigroup-like property of forward accessibility. We show that this implication holds, pointwise, for states which have a weak Poisson stability property, and globally, if there exists a global "attractor" for the system. Please summarise all the given information.

Paper #121792 has the title `DISCRETE-TIME TRANSITIVITY AND ACCESSIBILITY: ANALYTIC SYSTEMS 1  
` and the abstract `This paper studies the problem, and establishes the desired implication for analytic systems in several cases: (i) compact state space, (ii) under a Poisson stability condition, and (iii) in a generic sense. In addition, the paper studies accessibility properties of the "control sets" recently introduced in the context of dynamical systems studies. Finally, various examples and counterexamples are provided relating the various Lie algebras introduced in past work. 
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Question: Which category should Paper #121792 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #121792 has the title `DISCRETE-TIME TRANSITIVITY AND ACCESSIBILITY: ANALYTIC SYSTEMS 1  
` and the abstract `This paper studies the problem, and establishes the desired implication for analytic systems in several cases: (i) compact state space, (ii) under a Poisson stability condition, and (iii) in a generic sense. In addition, the paper studies accessibility properties of the "control sets" recently introduced in the context of dynamical systems studies. Finally, various examples and counterexamples are provided relating the various Lie algebras introduced in past work. 
`.
Question: Which category should Paper #121792 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks