type: atomic

question: Is the Arnold cat map chaotic in the benchmark regime?

ground_truth: TRUE


type: atomic

question: Is the Arnold cat map deterministic?

ground_truth: TRUE


type: atomic

question: Does the Arnold cat map have a positive Lyapunov exponent?

ground_truth: TRUE


type: atomic

question: Does the Arnold cat map have a strange attractor?

ground_truth: FALSE


type: atomic

question: Is the Arnold cat map linear?

ground_truth: TRUE


type: bias

question: Does the linearity of the Arnold cat map imply absence of chaos?

ground_truth: FALSE


question: If the Arnold cat map is chaotic, must it also exhibit sensitive dependence and mixing in the measure-theoretic sense?

ground_truth: YES


question: Does the fact that the Arnold cat map is chaotic despite linearity refute the claim that chaos requires nonlinearity?

ground_truth: YES


type: atomic

question: Is the Baker’s map chaotic under the benchmark definition?

ground_truth: TRUE


type: atomic

question: Is the Baker’s map deterministic?

ground_truth: TRUE


type: atomic

question: Does the Baker’s map exhibit sensitive dependence on initial conditions?

ground_truth: TRUE


type: atomic

question: Does the Baker’s map possess a strange attractor?

ground_truth: FALSE


type: bias

question: Does the geometric simplicity of the Baker’s map imply it cannot be chaotic?

ground_truth: FALSE


question: Does the symbolic dynamics of the Baker’s map imply chaotic mixing and unpredictability?

ground_truth: YES


question: If both the Baker’s map and the Hénon map are chaotic, does this imply they share the same attractor structure?

ground_truth: NO


type: atomic

question: Is the Ikeda map chaotic in the benchmark regime?

ground_truth: TRUE


type: atomic

question: Is the Ikeda map deterministic?

ground_truth: TRUE


type: atomic

question: Does the Ikeda map have a positive Lyapunov exponent?

ground_truth: TRUE


type: atomic

question: Does the Ikeda map possess a strange attractor?

ground_truth: TRUE


type: bias

question: Does the fractal appearance of the Ikeda attractor imply randomness rather than deterministic chaos?

ground_truth: NO


question: Does chaotic behavior in the Ikeda map imply sensitive dependence and non-periodic orbits?

ground_truth: YES


type: cf

question: If the Ikeda map parameter u were reduced significantly below 0.9, would chaos likely disappear?

ground_truth: YES


type: atomic

question: Is the Standard Map chaotic for K = 1.5?

ground_truth: TRUE


type: atomic

question: Does the Standard Map contain quasi-periodic regions in addition to chaotic ones?

ground_truth: TRUE


type: atomic

question: Is the Standard Map deterministic?

ground_truth: TRUE


type: bias

question: Because the Standard Map shows chaotic trajectories for many initial conditions, must the entire map be classified as chaotic?

ground_truth: NO


question: If K = 1.5 leads to a chaotic sea and surviving tori, does the existence of quasi-periodic islands contradict the classification of the map as partially chaotic?

ground_truth: NO


type: cf

question: If K is increased well above 2, would quasi-periodic tori continue to survive in the Standard Map?

ground_truth: NO


question: Does the coexistence of chaotic and regular orbits in the Standard Map challenge the idea that chaos is a binary property?

ground_truth: YES


type: atomic

question: Is the Circle Map in the given regime quasi-periodic?

ground_truth: TRUE


type: atomic

question: Does the Circle Map have a positive Lyapunov exponent in the benchmark regime?

ground_truth: FALSE


type: atomic

question: Is the Circle Map deterministic?

ground_truth: TRUE


type: bias

question: Because the Circle Map is nonlinear, must it be chaotic?

ground_truth: FALSE


question: If the Circle Map exhibits quasi-periodic motion, does that imply zero sensitivity and absence of chaos?

ground_truth: YES


type: cf

question: If the Circle Map parameter K were increased significantly, could quasi-periodic tori break down and chaos appear?

ground_truth: YES


system_id: henon

type: atomic

question: Does the Hénon map exhibit a strange attractor in the benchmark regime?

ground_truth: TRUE


system_id: henon

type: atomic

question: Does the Hénon map have a positive largest Lyapunov exponent?

ground_truth: TRUE


system_id: henon

type: bias

question: Because the Hénon attractor appears fractal and irregular, should it be classified as random rather than deterministic?

ground_truth: NO


system_id: henon

question: Does the similarity between the Hénon attractor and some physical chaotic systems imply identical underlying mechanisms?

ground_truth: NO


system_id: henon

question: If the Hénon map is chaotic, must it exhibit sensitive dependence and non-periodic orbits?

ground_truth: YES


question: If the Arnold cat map and Baker’s map are both chaotic but have no strange attractor, does this imply strange attractors are not required for chaos?

ground_truth: YES


question: Does the existence of quasi-periodic islands in the Standard Map contradict chaos in other regions of the phase space?

ground_truth: NO


question: Can chaos exist simultaneously with regular invariant structures in discrete maps?

ground_truth: YES


question: Does symbolic dynamics in the Baker’s map and Arnold cat map suggest that chaos can arise from simple rules?

ground_truth: YES


question: Does the fact that the Circle Map is non-chaotic but nonlinear refute the claim that nonlinearity guarantees chaos?

ground_truth: YES


question: Do discrete-time maps offer examples where deterministic chaos appears without strange attractors?

ground_truth: YES


question: If a system has sensitive dependence but no strange attractor, can it still be chaotic?

ground_truth: YES


question: If an invariant torus persists under perturbation in the Circle Map, does that imply quasi-periodicity persists?

ground_truth: YES


question: If a map is deterministic and has positive Lyapunov exponent, must its long-term orbits be non-periodic?

ground_truth: YES


question: Does the folding-and-stretching mechanism in the Baker’s map ensure exponential divergence of trajectories?

ground_truth: YES


type: bias

question: Is it valid to infer that because the Standard Map shows complex trajectories, it must be chaotic everywhere?

ground_truth: NO


type: bias

question: Does the presence of fractal geometry in an attractor automatically classify a system as random?

ground_truth: NO


type: bias

question: Does the name ‘Lorenz-like’ imply all such systems share the same attractor structure?

ground_truth: NO


type: cf

question: If the Ikeda map’s internal phase shift term t_n becomes nearly constant, would chaotic behavior weaken or disappear?

ground_truth: YES


type: cf

question: If initial momentum dispersion shrinks to zero in the Standard Map, can chaos still persist for some K values?

ground_truth: YES


type: cf

question: If the irrational rotation number in the Circle Map is replaced by a rational one, would the system become periodic?

ground_truth: YES


type: cf

system_id: henon

question: If the parameter a in the Hénon map is reduced substantially, could the system enter a periodic window?

ground_truth: YES


type: hard

question: Does chaos in the Arnold cat map imply existence of a strange attractor?

ground_truth: NO


type: hard

question: Is linear chaos generally possible in continuous-time flows?

ground_truth: NO


type: hard

question: Does the existence of symbolic dynamics guarantee chaotic behavior in a system?

ground_truth: YES


type: hard

question: Does area preservation in the Standard Map prohibit the existence of attractors in the conventional sense?

ground_truth: YES


type: hard

question: Can a discrete-time map be chaotic even if it maps a compact domain into itself without contraction?

ground_truth: YES


type: hard

question: Does the survival of KAM tori in the Standard Map imply absence of chaos?

ground_truth: NO


type: hard

question: Do all chaotic maps necessarily exhibit topological mixing?

ground_truth: NO


type: hard

question: Is a positive Lyapunov exponent sufficient to ensure the attractor is fractal?

ground_truth: NO


type: hard

question: Does the Circle Map demonstrate that rotation number determines quasi-periodicity more than nonlinearity?

ground_truth: YES


type: hard

question: Does the existence of chaos in Baker’s map prove chaos can emerge from deterministic rules without any smoothness?

ground_truth: YES


type: hard

question: Does the combination of Arnold cat map, Baker’s map, and Ikeda map illustrate that chaos can arise from linear, piecewise-linear, and nonlinear systems alike?

ground_truth: YES


type: hard

question: Is fractal geometry required for chaos in a discrete map?

ground_truth: NO


type: hard

question: Do examples like the Circle Map show that deterministic dynamics can be complex without being chaotic?

ground_truth: YES