This dissertation presents geometric approaches of understanding chaotic transport in phase space that is fundamental across many disciplines in physical sciences and engineering. This approach is based on analyzing phase space transport using boundaries and regions inside these boundaries in presence of perturbation. We present a geometric view of defining such boundaries and study the transport that occurs by crossing such phase space structures. The structure in two dimensional non-autonomous system is the codimension 1 stable and unstable manifolds associated with the hyperbolic fixed points. The manifolds separate regions with varied dynamical fates and their time evolution encodes how the initial conditions in a given region of phase space get transported to other regions. In the context of four dimensional autonomous systems, the corresponding structure is the stable and unstable manifolds of unstable periodic orbits which reside in the bottlenecks of energy surface. The total energy and the cylindrical (or tube) manifolds form the necessary and sufficient condition for global transport between regions of phase space. Furthermore, we adopt the geometric view to define escaping zones for avoiding transition/escape from a potential well using partial control. In this approach, the objective is two fold: finding the minimum control that is required for avoiding escape and obtaining discrete representation called disturbance of continuous noise that is present in physical sciences and engineering. In the former scenario, along with avoiding escape, the control is constrained to be smaller than the disturbance so that it can not exactly cancel out the disturbances. / Ph. D. / The prediction and control of critical events in engineering systems has been a major objective of scientific research in recent years. The multifaceted problems facing the modern society includes critical events such as spread of pathogens and pollutants in atmosphere and ocean, capsize of boats and cruise ships, space exploration and asteroid collision, to name but a few. Although, at first glance they seem to be disconnected problems in different areas of engineering and science, however, they have certain features that are inherently common. This can be studied using the abstraction of phase space which can be thought of as the universe where all possible solutions of the governing equations, derived using principles of physics, live and evolve in time. The <i>phase space</i> can be just 2D, 3D or even infinite dimensional but the critical events manifest themselves as volumes of phase space, which represent solutions at a given instant of time, get transported from one region to another due to the underlying dynamics. This mathematical abstraction is called phase space transport and studied under the umbrella of dynamical systems theory. The geometric view of the solutions that live in the phase space provides insight into the mechanisms of how the critical events occur, and the understanding of these mechanisms is useful in deciding about control strategies. A slightly different view for understanding critical events is to consider a thought experiment where a ball is rolling on a multi-well surface or potential well. As the time evolves, the ball will escape from its initial well and roll into another well, and eventually start exploring all the wells in a seemingly unpredictable way. However, these unpredictable escape/transition can be studied systematically using methods of chaos and dynamical systems. The escape/transition in a potential well implies a dramatic change in the behavior of the system, and hence the significance in prediction and control of <i>escaping dynamics</i>. The control aspect becomes more challenging due to inherent disturbance in the system that is difficult to model and we may not have the equal or more control authority to cancel those disturbances. However, we can usually estimate the maximum values of the disturbance, and try to avoid escaping from the potential well while using a smaller control. This idea is called <i>partial control of escaping dynamics</i> and can guarantee avoidance of escape for <i>ad infinitum</i>. In this doctoral research, we focus on the two mechanisms, phase space transport and escaping dynamics, by considering problems from fluid dynamics and capsize of a ship. The applications are used for numerical demonstration and evidence of the general approach in studying a large class of problems in classical physics.

Background: We live in a world where not everyone is employed; numerous people havelost their jobs due to several factors where one of them is the economic crisis. This has hada huge impact on Sweden and the unemployment rate. Previous research has shown thatinflation, unemployment, and high interest rates represent risks to consumer welfare. We all consume daily, or on occasions, but how do unemployed consumers consume, what do they consume and why? In this area, the authors have found a knowledge gap in literature; therefore exploring this phenomenon is of interest.   Purpose: The purpose of this study is to explore and illustrate how consumers who have experienced a life transition, from employment to unemployment, are affected by this and how it has an impact on their consumption.   Method: This is an exploratory study performed with a qualitative and an abductive approach, where the authors used primary data collection through semi-structured in-depth interviews in Swedish with 16 unemployed consumers. These unemployed consumers were selected at Arbetsförmedlingen, the public employment service, in Jönköping.   Results: By living in unemployment the consumers have been affected psychologically, physically, financially and socially. Their identity has changed for each of them since they have to adapt to the new circumstances in their life. The new life situation has had an impact on the consumer’s well-being where depression, anxiety, and a feeling of being the underdog in the society is present. Their new life situation has implied a change in their consumption behavior since they nowadays have to prioritize the basic needs. Many of the respondents used explicit and implicit shopping-list in order to reduce their impulse buying. The contribution that the authors have done to the theory of resistance is a fourth category called ‘Everyday life resistance’ which explains the behavior of people who live in unemployment, i.e. they always have to think about resisting temptations, wants, desires, and avoiding situations where the result may be unnecessary consumption. The consumers in this study are highly involved in their consumption behavior, which the authors have chosen to call ‘reversed habitual decision making’. This kind of involvement is very high despite the high- or low risk category of the product. Their new life situation has made them more aware of product alternatives, market supply, prices, and also knowledge about their own resistance in the marketplace. / Bakgrund: Vi lever i en värld där inte alla har en anställning, en omfattande andel av befolkningen har förlorat sitt jobb på grund av flera faktorer, där en av dem är den ekonomiska krisen. Detta har haft en stor påverkan på Sverige och dess arbetslöshet. Föregående studier har visat att inflation, arbetslöshet och hög räntesats representerar risk för konsumentens välbefinnande. Vi alla konsumerar dagligen eller vid speciella tillfällen, men hur konsumerar en arbetslös konsument, vad konsumerar dem och varför? Inom detta område har författarna funnit ett kunskaps gap i litteraturen, därav är en undersökning av detta fenomen av intresse.   Syfte: Syftet med denna studie är att utforska och illustrera hur konsumenter som har genomgått en livsförändring, från att ha varit anställd till att vara arbetslös, är påverkade av detta och hur detta har inverkat på deras konsumtion.   Metod: Detta är en explorativ studie genomförd med en kvalitativ och abduktiv tillvägagångssätt där författarna har använt sig av primär information samlad genom, till viss del, strukturerade djupgående intervjuer på svenska med 16 arbetslösa konsumenter. Dessa var utvalda vid Arbetsförmedlingen i Jönköping.   Resultat: Att leva som arbetslös har påverkat konsumenterna psykologiskt, fysiskt, finansiellt och socialt. Deras identitet har förändrats då de måste anpassa sig till den nya livssituationen. Den nya situationen har påverkat konsumenternas hälsa då de känner av depression, ängslan och känner sig mindre värda i samhället. Deras nya livssituation har inneburit en det förändringar i deras konsument beteende eftersom de numera måste prioritera sina primära behov. Många av studiens deltagare använde sig av explicita och implicita inköpslistor för att minimera spontanköp. Författarnas bidrag till teorin om motstånd är en fjärde kategori kallad ‘Vardagligt motstånd’ vilket förklarar beteendet hos arbetslösa personer dvs. de måste hela tiden tänka på att motstå frestelser, begär och försöka undvika situationer där onödiga inköp kan uppstå. Konsumenterna i denna studie är synnerligen involverade i sitt konsument beteende, detta har författarna valt att benämna ’omvänt rutin besluts genomförande’. Denna typ av involvering är väldigt hög oavsett om produktkategorin innebär hög- eller låg risk. Deras nya livssituation har gjort dem mer medvetna om alternativa produkter, marknadens utbud, priser och ny kunskap om deras egna motstånd inom konsumtionssamhället.

<p><strong>Background:</strong> We live in a world where not everyone is employed; numerous people havelost their jobs due to several factors where one of them is the economic crisis. This has hada huge impact on Sweden and the unemployment rate. Previous research has shown thatinflation, unemployment, and high interest rates represent risks to consumer welfare. We all consume daily, or on occasions, but how do unemployed consumers consume, what do they consume and why? In this area, the authors have found a knowledge gap in literature; therefore exploring this phenomenon is of interest.</p><p> </p><p><strong>Purpose:</strong> The purpose of this study is to explore and illustrate how consumers who have experienced a life transition, from employment to unemployment, are affected by this and how it has an impact on their consumption.</p><p> </p><p><strong>Method:</strong> This is an exploratory study performed with a qualitative and an abductive approach, where the authors used primary data collection through semi-structured in-depth interviews in Swedish with 16 unemployed consumers. These unemployed consumers were selected at Arbetsförmedlingen, the public employment service, in Jönköping.</p><p> </p><p><strong>Results:</strong> By living in unemployment the consumers have been affected psychologically, physically, financially and socially. Their identity has changed for each of them since they have to adapt to the new circumstances in their life. The new life situation has had an impact on the consumer’s well-being where depression, anxiety, and a feeling of being the underdog in the society is present. Their new life situation has implied a change in their consumption behavior since they nowadays have to prioritize the basic needs. Many of the respondents used explicit and implicit shopping-list in order to reduce their impulse buying. The contribution that the authors have done to the theory of resistance is a fourth category called ‘Everyday life resistance’ which explains the behavior of people who live in unemployment, i.e. they always have to think about resisting temptations, wants, desires, and avoiding situations where the result may be unnecessary consumption. The consumers in this study are highly involved in their consumption behavior, which the authors have chosen to call ‘reversed habitual decision making’. This kind of involvement is very high despite the high- or low risk category of the product. Their new life situation has made them more aware of product alternatives, market supply, prices, and also knowledge about their own resistance in the marketplace.</p> / <p><strong>Bakgrund:</strong> Vi lever i en värld där inte alla har en anställning, en omfattande andel av befolkningen har förlorat sitt jobb på grund av flera faktorer, där en av dem är den ekonomiska krisen. Detta har haft en stor påverkan på Sverige och dess arbetslöshet. Föregående studier har visat att inflation, arbetslöshet och hög räntesats representerar risk för konsumentens välbefinnande. Vi alla konsumerar dagligen eller vid speciella tillfällen, men hur konsumerar en arbetslös konsument, vad konsumerar dem och varför? Inom detta område har författarna funnit ett kunskaps gap i litteraturen, därav är en undersökning av detta fenomen av intresse.</p><p> </p><p><strong>Syfte:</strong> Syftet med denna studie är att utforska och illustrera hur konsumenter som har genomgått en livsförändring, från att ha varit anställd till att vara arbetslös, är påverkade av detta och hur detta har inverkat på deras konsumtion.</p><p> </p><p><strong>Metod:</strong> Detta är en explorativ studie genomförd med en kvalitativ och abduktiv tillvägagångssätt där författarna har använt sig av primär information samlad genom, till viss del, strukturerade djupgående intervjuer på svenska med 16 arbetslösa konsumenter. Dessa var utvalda vid Arbetsförmedlingen i Jönköping.</p><p> </p><p><strong>Resultat:</strong> Att leva som arbetslös har påverkat konsumenterna psykologiskt, fysiskt, finansiellt och socialt. Deras identitet har förändrats då de måste anpassa sig till den nya livssituationen. Den nya situationen har påverkat konsumenternas hälsa då de känner av depression, ängslan och känner sig mindre värda i samhället. Deras nya livssituation har inneburit en det förändringar i deras konsument beteende eftersom de numera måste prioritera sina primära behov. Många av studiens deltagare använde sig av explicita och implicita inköpslistor för att minimera spontanköp. Författarnas bidrag till teorin om motstånd är en fjärde kategori kallad ‘Vardagligt motstånd’ vilket förklarar beteendet hos arbetslösa personer dvs. de måste hela tiden tänka på att motstå frestelser, begär och försöka undvika situationer där onödiga inköp kan uppstå. Konsumenterna i denna studie är synnerligen involverade i sitt konsument beteende, detta har författarna valt att benämna ’omvänt rutin besluts genomförande’. Denna typ av involvering är väldigt hög oavsett om produktkategorin innebär hög- eller låg risk. Deras nya livssituation har gjort dem mer medvetna om alternativa produkter, marknadens utbud, priser och ny kunskap om deras egna motstånd inom konsumtionssamhället.</p>