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Abstract The Weyl type f(Q, T) gravity is the modification of f(Q) gravity and f(Q, T) theories, where non-metricity is denoted by Q and T is the trace of the energy–momentum tensor. Together with a geometric explanation for dark energy, the theory can provide an exact interpretation of the transformation of the late-time Universe and the observable data. In this study, we present an accelerated cosmic model of the Universe in f(Q, T) gravity. We consider the model of f(Q, T) gravity as, $$f(Q,T) = -Q+\phi (Q,T)$$ f ( Q , T ) = - Q + ϕ ( Q , T ) . We examine the energy condition for the model of f(Q, T) gravity and find out that our model satisfies the null and strong energy conditions at the same time, it violates the weak and dominant energy conditions. After that, we perform the phase-space study of our cosmological model with and without interaction independently. In case of the absence of interaction, we get six critical points out of which three critical points are stable critical points while the rest three critical points are saddle. When we perform the stability analysis in the presence of interaction, we get three critical points out of which one critical point is stable while the rest two are saddle points. The phase-plot analysis also shows the cosmological models in f(Q, T) gravity.

In this study, the Universe's rip cosmology theories have been provided for the f(Q,C) gravity theory, where Q and C stand for the non-metricity scalar and boundary term. We assume f(Q,C)=αQn+βC and analyze the nature of the physical parameters for the Little Rip (LR), Big Rip (BR) and Pseudo Rip (PR) models. In the LR and PR models, the EoS parameter exhibits phantom characteristics but remains closely aligned with the ΛCDM line. The non-metricity term Q has direct effect on the rip models. After investigating the energy conditions, we recognise that our model violates the strong energy constraint. Avoiding singularity situations has been noted in all of these accelerated models. The characteristics of the jerk and snap parameters have been investigated. Our model provides an effective description of the Universe's evolutionary history and fits well with contemporary cosmic data.

In this work, we discussed the Davies-type phase transitions in two distinct categories of dyonic AdS black holes (BHs). The first one is dyonic AdS BHs within four-dimensional spacetime framework. The second one is the dyonic BHs with quasitopological electromagnetism (QE) in Einstein-Gauss-Bonnet gravity (EGBG). First, we analyze the increasing and decreasing behavior of divergency depending upon different parameters which provides useful information about the region that are physical and stable. We also discuss the critical behavior of BHs in three different statistical ensembles: the canonical, mixed and grand canonical. It is noted that BHs can be classified into distinct topological classes based on their topological charge (Q) which assumes discrete values of 0,+1,−1. This topological charge plays a pivotal role in determining the phase structure and stability of the BHs within each ensemble. A topological charge of 0 corresponds to a neutral topological state that could be indicative of a more complex underlying structure, while charges of +1 or −1 indicate the presence of additional structures such as magnetic monopoles or dyons, which significantly influence the thermodynamic properties and phase transitions of the system.

In this paper, we investigate the impact of the oblateness of the secondary body on the motion of a test particle in the near vicinity of the secondary body, specifically in the context of the extended version of the planar Hill problem. To achieve this objective, we conduct a comprehensive survey by systematically classifying the initial conditions of trajectories and scanning the phase space using two-dimensional (2D) maps on various planes. We then numerically integrate the starting conditions on these maps and classify the final states of the test particles as either bounded or unbounded. Bounded orbits are further subclassified as collision orbits and regular (or chaotic), while unbounded orbits are sub-classified according to the sector of the (x,y) plane through which the particle escapes the potential well. Our results reveal that increasing values of the oblateness coefficient reduce the number of escaping orbits and limit the extension of islands of regular motion (in the Liouville–Arnold sense). Regular bounded motion occurs only at larger distances from the secondary body.

We investigate the orbital dynamics of an exosystem consisting of a solar-mass host star, a transiting body, and an Earth-size exoplanet within the framework of the generalized three-body problem. Depending on its mass, the transiting body can either be a super-Jupiter or a brown dwarf. To determine the final states of the Earth-size exoplanet, we conduct a systematic and detailed classification of the available phase space trajectories. Our classification scheme distinguishes between the bounded, escape, and collisional motions of the Earth-size exoplanet. Additionally, for cases of ordered (regular) motion, we further categorize the associated initial conditions based on the geometry of their respective trajectories. These bounded regular trajectories hold significant importance as they provide insights into the regions of phase space where the motion of the Earth-size exoplanet can be dynamically stable. Of particular interest is the identification of initial conditions that result in a bounded exomoon-like orbit of the Earth-size exoplanet around the transiting body.

We consider the motion of a test particle (star) on the meridian plane (R,z) of an elliptical galaxy with an additional central nucleus component. The shape of the elliptical galaxy can be either prolate or oblate, or even spherical by simply changing the numerical value of the flattening parameter entering the equation of the potential of the elliptical galaxy. By means of numerical integration of both the motion equations and the equations of variations of the system, we conduct a systematic orbit classification of the starting conditions of the test particle, thus revealing how the flattening parameter affects its orbital dynamics. Our simulations suggest that in the scenario where the elliptical galaxy has a prolate shape the motion of a star is much more complicated with respect to the case where we have a usual oblate elliptical galaxy. Additionally, we also investigate how the total orbital energy of the test particle affects its dynamics in relation to the flattening parameter of the elliptical galaxy.

In this paper, the equilibrium dynamics of the circular restricted (2+1)-body problem with two elongated main bodies is investigated. More precisely, the influence of the mass parameter and the non-sphericity parameter on the position and stability of the libration points of this characteristic configuration is studied through numerical and semi-analytical methods. In addition, the effect of these two parameters of the system on the fractality of the basins of convergence is also investigated, for this, two quantitative indicators are used: the boundary basin entropy and the uncertainty dimension. It is shown that when the two objects have the same value of the non-sphericity parameter, the appearance of new collinear and non-collinear libration points takes place. Compared to the classical circular restricted three-body problem, our numerical study reveals that when both primaries are prolate, some of the collinear libration points may be stable.

We consider a Hamiltonian system associated with the two-well umbilical catastrophe potential D5, while the corresponding potential contains only one free parameter. We determine how this free parameter affects the equilibrium dynamics of the system by computing their coordinates on the configuration plane, along with their linear stability and type. Additionally, we discuss the influence of the same free parameter on the orbital dynamics of the system by performing a systematic and thorough orbit classification that allows us to reveal the bounded or escaping motion of the test particle.

The main goal of this work is to elucidate the effect of the inclusion of a rigid triaxial prolate primary body on the dynamics of the circular restricted three-body problem. The position, type, and linear stability of the coplanar points of equilibria are determined by numerical methods. Specifically, we conduct a systematic numerical study for elucidating the influence on the dynamics of the system of the triaxial prolate shape. Our findings are conclusive and indicate that the triaxiality parameters are very influential on the equilibria of the system, modifying not only the total number of equilibrium points but also their stability and nature. We also compare our findings with those of the previous paper of the series, where we have studied the case of triaxial oblate primary bodies.

Our work is aimed to investigate the equilibrium dynamics of the restricted three-body problem with equally massed prolate radiating bodies. The positions along with the linear stability of the coplanar points of equilibrium are determined by using numerical methods. In particular, we conduct a systematic and rigorous analysis for revealing the influence of the prolateness coefficient A and the radiation pressure factor q on the dynamics of the system. Our results indicate that both these two parameters are highly influential on the equilibria of the system.

We deploy the theory of the generalized three-body problem to describe an exosystem composed of a host star, a transiting Jupiter-sized exoplanet, and an Earth-sized exoplanet. By performing a thorough and systematic orbit classification we map a large section of the phase space and determine the final states of the Earth-sized exoplanet. In particular, we manage to classify the initial conditions of the perturber into several categories such as bounded regular or chaotic motion, collision, and escaping motion. Bounded regular motion corresponds to regions of the phase space in which the orbit of the Earth-sized planet would be stable. In our computations, we use realistic values of the involved parameters and initial conditions corresponding to real observable exosystems. Our analysis provides important information on how the mass of the host star as well as the mass of the Jupiter size affects the orbital dynamics of the Earth-sized exoplanet.

The restricted three-body problem, with a rigid triaxial oblate primary body, is being under investigation. Using numerical methods we reveal how the triaxility parameters affect the coordinates and the linear stability of the libration points. We perform a systematic and rigorous analysis for understanding the effect of the parameters σ1and σ2on the dynamical properties of the system. Our study suggests that these parameters have a strong impact on the dynamics of the equilibrium points of the system.

This article aims to investigate the points of equilibrium and the associated convergence basins in a seventh-order generalized Hénon–Heiles potential. Using the well-known Newton–Raphson iterator, we numerically locate the positions of the points of equilibrium, while we also obtain their linear stability. Furthermore, we demonstrate how the two variable parameters, entering the generalized Hénon–Heiles potential, affect the convergence dynamics of the system as well as the fractal degree of the basin diagrams. The fractal degree is derived by computing the (boundary) basin entropy as well as the uncertainty dimension.

This letter deals with the derivation and analysis of a seventh-order generalization of the Hénon-Heiles potential. The new potential has axial and reflection symmetries, and finite escape energy with three channels of escape. Based on SALI indicator and exits basins, the dynamic behavior of the seventh-order system is investigated qualitatively in cases of bounded and unbounded movement. Moreover, a quantitative analysis is carried out through the percentage of chaotic orbits and the basin entropy, respectively. After classifying large sets of initial conditions of orbits for several values of the energy constant in both regimes, we observe that when the energy moves away from the critical value, the chaoticity of the system decreases and the basin structure becomes simpler with sharper and well defined bounds. Our results suggest that when the seventh-order contributions of the potential are taken into account, the system becomes less ergodic in comparison with the classical version of the Hénon-Heiles system.