https://popups.uliege.be/3041-539x/index.php?id=2254 Index terms fr 0 https://popups.uliege.be/3041-539x/index.php?id=2994 Consistent structure of a Hamiltonian dynamical system with constant energy is shown in terms of category theory. A colimit of the dynamical system corresponds to a set of pairs of an initial state and a final state. Expansion of the colimit based on a concept of internal measurement induces heterarchical structure in the dynamical system and derives interaction between the system and the other one. Dynamical change of potential functions derived from that expansion is relevant to a concept of emergence based on the viewpoint of the Hamiltonian system. Wed, 04 Sep 2024 09:24:35 +0200 Wed, 04 Sep 2024 09:24:55 +0200 https://popups.uliege.be/3041-539x/index.php?id=2994 https://popups.uliege.be/3041-539x/index.php?id=2857 Nonlinear dynamical systems show some different motions such as periodic, chaotic or intermittent ones. On-off intermittency is aperiodic switching motion between laminar phases and burst phases. It is observed in critical points with blowout bifurcation. Occurrence of it is sensitive with respect to parameter shifts in conventional systems. In the present paper, an extended dynamical system with an interaction between a global structure and a local motion is proposed. This interaction means a reciprocal definition between a parameter and state variables. The reciprocal definition is induced from the concept of a generative pointer that suggests an extended subobject classifier. Ubiquitous on-off intermittency is observed for a wide range of parameter values when a generative pointer is applied to a Henon map. This fact implies robustness of on-off intermittency against parameter shifts. Tue, 03 Sep 2024 15:24:24 +0200 Tue, 03 Sep 2024 15:24:31 +0200 https://popups.uliege.be/3041-539x/index.php?id=2857 https://popups.uliege.be/3041-539x/index.php?id=2253 It has been recognized that there are two kinds of cognitive maps, route map and survey map. Researchers recently have focused on the integration of both maps. The attempt to integrate them, however, entails a problem ; which type is prior to the other. This reveals an infinite regression. We propose that the paradoxical modality resulting from the integration can be expressed as a heterarchy, a dynamical hierarchical system. In the name of heterarchy, we stress negotiation among levels. If there is a discrepancy between levels, the expression of a level and interaction are destined to contain intrinsic indefiniteness. It reveals the negotiation. Route maps and survey maps are not integrated but negotiated, and those form a heterarchy. We conducted a particular experiment in which negotiations between route maps and survey maps were enhanced. Tue, 30 Jul 2024 15:41:31 +0200 Tue, 30 Jul 2024 15:41:39 +0200 https://popups.uliege.be/3041-539x/index.php?id=2253